Math worksheets for practicing number sequences and pattern recognition.

Let’s solve each part of the “Super Sequences” worksheet step by step. We’ll go section by section, find the rule for each sequence, and fill in the missing numbers.

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Left Column – Top Section:

*Sequence 1: 6573, ____, 6583, ____, 6603*

Look at the known numbers:
6573 → ? → 6583 → ? → 6603

From 6573 to 6583 is +10.
If we add 10 again: 6583 + 10 = 6593
Then 6593 + 10 = 6603 — that matches!

So the pattern is +10.

Missing numbers:
After 6573: 6573 + 10 = 6583 (already given)
Wait — actually, the blanks are after 6573 and after 6583.

Given:
Position 1: 6573
Position 2: ___
Position 3: 6583
Position 4: ___
Position 5: 6603

So from pos1 to pos3: 6573 → 6583 = +10 over two steps → so each step is +5? Let’s check:

Try +5:
6573 + 5 = 6578
6578 + 5 = 6583 ✔
6583 + 5 = 6588
6588 + 5 = 6593 → but next given is 6603, not 6593 ✘

Wait — maybe it’s +10 every other step? No, let’s look again.

Actually, from 6573 to 6583 is +10, then 6583 to 6603 is +20 — that doesn’t help.

Wait — perhaps I misread. The sequence is written as:

“6573, ____, 6583, ____, 6603”

That’s five terms total. So positions:

1: 6573
2: ?
3: 6583
4: ?
5: 6603

Difference between term 1 and term 3: 6583 - 6573 = 10 → over 2 steps → so +5 per step.

Check:
Term 1: 6573
Term 2: 6573 + 5 = 6578
Term 3: 6578 + 5 = 6583 ✔
Term 4: 6583 + 5 = 6588
Term 5: 6588 + 5 = 6593 — but the last term is 6603, not 6593

Hmm… contradiction.

Wait — maybe it’s not arithmetic? Or maybe typo? But let’s try another approach.

What if the jump from term 3 to term 5 is +20? 6583 to 6603 is +20 over 2 steps → +10 per step.

But then term 1 to term 3 should also be +20? 6573 to 6583 is only +10.

Inconsistent.

Wait — perhaps the sequence is:

6573, [blank], 6583, [blank], 6603

Maybe it’s increasing by 10, then 10, then 20? That seems odd.

Alternative idea: Maybe it’s +10, then +10, then +20? Not consistent.

Wait — let’s calculate differences:

Assume constant difference.

Let d = common difference.

Term1: a = 6573
Term3: a + 2d = 6583 → 6573 + 2d = 6583 → 2d = 10 → d = 5

Then Term5: a + 4d = 6573 + 20 = 6593 — but given as 6603 → off by 10.

Unless... the last number is wrong? Unlikely.

Wait — perhaps I misread the sequence. Let me re-express:

The problem says: “Sequence 1: 6573, ____, 6583, ____, 6603”

Maybe it’s not equally spaced? But sequences usually are.

Another thought: Perhaps it’s +10, then +10, then +20? But that’s not a standard sequence.

Wait — what if it’s +5, +5, +10, +10? Still messy.

Let’s skip and come back.

Actually, looking ahead — Sequence 2 might give us a clue.

*Sequence 2: 196, ____, 1966, ____, 1996*

Again, 5 terms.

Term1: 196
Term3: 1966
Term5: 1996

From term1 to term3: 1966 - 196 = 1770 over 2 steps → 885 per step? Too big.

196 to 1966 is +1770? That can’t be right for a simple sequence.

Wait — perhaps it’s 196, then something, then 1966 — maybe it’s adding 10s or 100s.

196 to 1966: that’s like adding 1770 — unlikely.

Perhaps it’s a typo? Or maybe it’s 196, 1966, 1996 — but there are blanks.

Another idea: Maybe the numbers are grouped differently.

Wait — let’s look at the third sequence on left column.

*Sequence 3: 18720, ____, 19700, ____, 20680*

Term1: 18720
Term3: 19700
Term5: 20680

From term1 to term3: 19700 - 18720 = 980 over 2 steps → 490 per step.

Then term3 to term5: 20680 - 19700 = 980 over 2 steps → same! So d = 490.

So for Sequence 3:

Term1: 18720
Term2: 18720 + 490 = 19210
Term3: 19210 + 490 = 19700 ✔
Term4: 19700 + 490 = 20190
Term5: 20190 + 490 = 20680 ✔

Perfect! So rule is +490.

Now back to Sequence 1: 6573, __, 6583, __, 6603

If we assume same logic: term1 to term3 is +10 over 2 steps → d=5

Then term5 should be 6573 + 4*5 = 6573+20=6593, but it's given as 6603 — which is 10 more.

Unless... the last number is 6593? But it's printed as 6603.

Perhaps it's +10 per step starting from second term? Let's try:

Suppose term2 = x, term3 = 6583, term4 = y, term5 = 6603

If from term3 to term5 is +20 over 2 steps, d=10.

Then term4 = 6583 + 10 = 6593
term5 = 6593 + 10 = 6603 ✔

Then what about term1 to term3? 6573 to 6583 is +10 over 2 steps, so d=5 for first part? Inconsistent.

Unless the sequence changes rule — but that's unusual for this level.

Another possibility: Maybe it's +10, then +10, then +20? But why?

Let's calculate the average increase.

Total from term1 to term5: 6603 - 6573 = 30 over 4 intervals → average 7.5 per step — not integer.

Not likely.

Perhaps it's a different pattern. Let's look at digits.

6573, ?, 6583, ?, 6603

From 6573 to 6583: tens digit increases by 1 (7 to 8), units same.

6583 to 6603: hundreds digit increases by 1 (5 to 6), tens from 8 to 0? 6583 to 6603 is +20, so tens digit goes 8 to 0 with carryover.

Not helping.

Wait — perhaps the blank after 6573 is 6578, and after 6583 is 6593, and the last is 6603 — but 6593 to 6603 is +10, so if we have:

6573, 6578 (+5), 6583 (+5), 6593 (+10), 6603 (+10) — still inconsistent.

I think there might be a mistake in my assumption. Let's move to Sequence 2 and see if it gives insight.

Sequence 2: 196, __, 1966, __, 1996

Term1: 196
Term3: 1966
Term5: 1996

196 to 1966 is +1770 — too big.

1966 to 1996 is +30.

Perhaps it's 196, then 1966 is a typo? Should be 196 + something small.

Another idea: Maybe it's 196, 1966, 1996 — but with blanks, so perhaps it's 196, x, 1966, y, 1996

If we assume linear, from term1 to term3: 1966 - 196 = 1770 over 2 steps → d=885

Then term2 = 196 + 885 = 1081
term4 = 1966 + 885 = 2851
term5 = 2851 + 885 = 3736 — but given as 1996, not matching.

Worse.

Perhaps the numbers are 196, 1966, 1996 — but 1966 is meant to be 196 + 10 = 206? No.

Let's read the numbers carefully. In the image, it might be "196, ____, 1966, ____, 1996" — but 1966 is four digits, others are three or four.

196 is three digits, 1966 is four, 1996 is four — so perhaps it's correct.

Another thought: Maybe it's not addition, but concatenation or something else — unlikely for this level.

Perhaps it's a geometric sequence? 196 to 1966 is roughly *10, but 196*10=1960, close to 1966.

196 * 10 = 1960, then 1960 +6 = 1966? Not clean.

Let's try to force it.

Suppose from term1 to term3: +1770, so d=885, but then term5 should be 196 + 4*885 = 196 + 3540 = 3736, not 1996.

No.

Perhaps the sequence is 196, 1966, 1996 — and the blanks are for intermediate, but with different rules.

I recall that in some worksheets, they have sequences where the increment changes, but usually specified.

Let's look at the middle column.

Middle column top: "Find the rule and give the next three terms for each of these sequences."

First sequence: 225, 450, 675, 900, 1125, ...

Clearly +225 each time.

225*1=225, 225*2=450, etc. So next three: 1125+225=1350, 1350+225=1575, 1575+225=1800.

Second sequence: 243.5, 243.8, 244.1, 244.4, 244.7, 245, ...

+0.3 each time.

Next three: 245 +0.3=245.3, 245.6, 245.9

Third sequence: 10.01, 10.01, 10.01, 10.01, 10.01, 10.01, ... — constant, so next three are all 10.01

Fourth: Add the missing terms in these sequences.

450 500, 450 900, 450 800, 450 700, 450 600 — wait, this looks like it's decreasing by 100 in the second part.

450 500, then 450 900? That would be increase, but then 450 800, etc.

Perhaps it's 450500, 450900, 450800, 450700, 450600 — but that doesn't make sense.

Looking at the text: "450 500, 450 900, 450 800, 450 700, 450 600" — probably it's 450,500; 450,900; etc., but that's not a sequence.

Perhaps it's a single number: 450500, 450900, 450800, 450700, 450600 — then the difference is -100 each time after the first? 450500 to 450900 is +400, then to 450800 is -100, not consistent.

Another idea: Perhaps it's 450, 500, 450, 900, 450, 800, etc. — alternating.

But the instruction is "add the missing terms", and it's listed as "450 500, 450 900, 450 800, 450 700, 450 600" — likely it's five terms: term1: 450500, term2: 450900, term3: 450800, term4: 450700, term5: 450600

Then from term2 to term5: 450900, 450800, 450700, 450600 — decreasing by 100.

But term1 to term2: 450500 to 450900 is +400, not fitting.

Perhaps the first is 450,500 meaning 450 and 500, but that doesn't help.

Let's look at the next one in middle column: "10.51, ____, 10.51, 17.01, 17.51, ____"

This is messy.

Perhaps I should focus on the right column, which might be clearer.

Right column top: "Find the rule and give the next three terms for each of these sequences."

First: 3448, 3548, 3648, 3748, 3848, 3948, ...

+100 each time. Next three: 4048, 4148, 4248

Second: 1101, 1101, 1143, 1185, 1227, 1269, ...

From 1101 to 1101: +0
1101 to 1143: +42
1143 to 1185: +42
1185 to 1227: +42
1227 to 1269: +42

So after the first repeat, it's +42. But the first two are both 1101, so perhaps it's a mistake, or the rule starts later.

Usually, sequences start from the beginning. From term2 to term3: +42, term3 to term4: +42, etc. So perhaps term1 is extra, or it's 1101, then 1101 (same), then +42 each.

But for next three, after 1269: 1269+42=1311, 1311+42=1353, 1353+42=1395

Third: "Find the rule and add the missing terms in these sequences. Draw arrows to help you."

First: 4560, 4560, ____, 1980, 2760, ...

4560, 4560, ?, 1980, 2760

From 4560 to 1980 is decrease, then to 2760 increase — not clear.

4560 to 1980 is -2580, then to 2760 is +780 — not nice.

Perhaps it's 4560, 4560, x, 1980, 2760

If we assume from term3 to term4 to term5 is arithmetic.

Suppose term4 = 1980, term5 = 2760, difference +780.

Then term3 = 1980 - 780 = 1200

Then term2 = 4560, term3 = 1200, difference -3360 — not good.

Another idea: Perhaps the numbers are related to multiples or factors.

4560 and 1980 — gcd? 4560 ÷ 120 = 38, 1980 ÷ 60 = 33, not helpful.

Let's calculate the difference between term4 and term5: 2760 - 1980 = 780

If the sequence is increasing by 780 from term3 onwards, then term3 = 1980 - 780 = 1200

Then from term2 to term3: 4560 to 1200 = -3360

From term1 to term2: 4560 to 4560 = 0

Not consistent.

Perhaps it's two interleaved sequences.

For example, odd positions: term1: 4560, term3: ?, term5: 2760

Even positions: term2: 4560, term4: 1980

Then for even positions: 4560, 1980 — difference -2580

For odd positions: 4560, ?, 2760 — if arithmetic, from 4560 to 2760 is -1800 over 2 steps, so -900 per step, so term3 = 4560 - 900 = 3660

Then the sequence would be: 4560, 4560, 3660, 1980, 2760

Check if it makes sense: from 4560 to 4560 (0), to 3660 (-900), to 1980 (-1680), to 2760 (+780) — not smooth.

Perhaps the rule is different.

Let's look at the last sequence in right column: "22 240, 22 700, 23 900, ____, 26 300"

Probably 22240, 22700, 23900, ?, 26300

Differences: 22700 - 22240 = 460
23900 - 22700 = 1200
Then to 26300 - 23900 = 2400 — not consistent.

460, 1200, 2400 — ratios 1200/460≈2.6, 2400/1200=2, not constant.

Perhaps it's +460, then +1200, then +2400, then +4800? But 23900 +2400 = 26300, yes! 23900 + 2400 = 26300.

So the increments are doubling: +460, +1200, +2400

But 460 to 1200 is not double; 460*2=920, not 1200.

1200 / 460 ≈ 2.608, not nice.

Another idea: Perhaps the numbers are 22,240; 22,700; 23,900; ?; 26,300

Let me write without commas: 22240, 22700, 23900, x, 26300

22700 - 22240 = 460
23900 - 22700 = 1200
26300 - 23900 = 2400

460, 1200, 2400 — notice that 1200 = 460 * 2 + 280? Not good.

460, then 1200 = 460 + 740, then 2400 = 1200 + 1200 — not helpful.

Perhaps it's based on place value.

Let's consider the difference between consecutive terms:

From 22240 to 22700: +460
22700 to 23900: +1200
23900 to x: ?
x to 26300: ?

And 26300 - 23900 = 2400, so if the increment doubles each time: +460, +920, +1840, but 460*2=920, 920*2=1840, then 22240 +460 = 22700, +920 = 23620, +1840 = 25460, then +3680 = 29140, not 26300.

Not matching.

From 22700 to 23900 is +1200, which is 460 * 2.608, not integer.

Another thought: Perhaps the numbers are 22,240; 22,700; 23,900; 25,100; 26,300 — then differences: 460, 1200, 1200, 1200 — but 23900 to 25100 is +1200, 25100 to 26300 is +1200, but from 22700 to 23900 is +1200, so from 22240 to 22700 is +460, then +1200 each time.

So the rule is: first increment +460, then +1200 thereafter.

So after 23900, next is 23900 +1200 = 25100, then 25100 +1200 = 26300 ✔

So missing term is 25100.

Great! So for that sequence, missing number is 25100.

Now back to left column.

Perhaps for Sequence 1: 6573, __, 6583, __, 6603

If we assume that from term3 to term5 is +20 over 2 steps, so +10 per step, so term4 = 6583 +10 = 6593, term5 = 6593 +10 = 6603.

Then from term1 to term3: 6573 to 6583 is +10 over 2 steps, so +5 per step, so term2 = 6573 +5 = 6578.

So the sequence is: 6573, 6578, 6583, 6593, 6603

But the increment changes from +5 to +10 after term3. Is that acceptable? In some contexts, yes, if not specified otherwise.

Similarly for Sequence 2: 196, __, 1966, __, 1996

If we apply the same logic: from term3 to term5: 1966 to 1996 is +30 over 2 steps, so +15 per step.

So term4 = 1966 +15 = 1981, term5 = 1981 +15 = 1996 ✔

From term1 to term3: 196 to 1966 is +1770 over 2 steps, so +885 per step.

So term2 = 196 +885 = 1081

Then sequence: 196, 1081, 1966, 1981, 1996

Increments: +885, +885, +15, +15 — still changes, but possible.

For Sequence 3 we already did: +490 each time, so 18720, 19210, 19700, 20190, 20680

Now for the Venn diagram part on left column.

It says: "These numbers shown appear in the correct cell above or in the correct diagram. If you need to, use the clues to work out where the numbers should be placed in the cells of the diagrams."

There is a Venn diagram with three circles: Sequence 1, Sequence 2, Sequence 3.

Numbers given: 1101, 300, 10823, 40100, 2660, 4500, 1710, 900

And the sequences are the ones we have.

But we have multiple sequences, so perhaps the Venn diagram is for classifying numbers into which sequences they belong to.

But the sequences are different types.

Perhaps the "sequences" refer to the patterns we found.

But it's complicated.

Perhaps for the Venn diagram, we need to see which numbers fit which sequence rules.

But let's first finish the sequences.

Also, in the middle column, there is "Add the missing terms in these sequences." with "450 500, 450 900, 450 800, 450 700, 450 600" — likely it's 450500, 450900, 450800, 450700, 450600, and the rule is that after the first, it decreases by 100: 450900, 450800, 450700, 450600, so the first is 450500, which is 400 less than 450900, so perhaps the missing term before is not needed, or it's given.

The instruction is "add the missing terms", and it's listed as five terms, so perhaps no missing, but the way it's written, "450 500, 450 900, ..." might mean that "450 500" is one number, etc.

Perhaps it's 450, 500, 450, 900, 450, 800, etc., but that would be six terms.

I think it's safer to assume that for Sequence 1 on left: 6573, 6578, 6583, 6593, 6603

For Sequence 2: 196, 1081, 1966, 1981, 1996

For Sequence 3: 18720, 19210, 19700, 20190, 20680

Now for the Venn diagram, the numbers are to be placed in the regions based on which sequences they satisfy.

But what are the sequences? Probably the three sequences we have, but they are specific instances.

Perhaps the "sequences" refer to the general rules.

For example, Sequence 1 has rule +5 then +10, but that's not standard.

Another idea: Perhaps the Venn diagram is for the numbers to be classified as belonging to arithmetic sequences with certain properties.

But let's look at the numbers: 1101, 300, 10823, 40100, 2660, 4500, 1710, 900

And the sequences are labeled Sequence 1,2,3, which are the ones we solved.

Perhaps we need to see if these numbers appear in any of the sequences we have.

For example, in Sequence 1: 6573, 6578, 6583, 6593, 6603 — none of the given numbers match.

Sequence 2: 196, 1081, 1966, 1981, 1996 — 1081 is close to 10823? No.

10823 is larger.

Sequence 3: 18720, 19210, 19700, 20190, 20680 — no match.

So probably not.

Perhaps the Venn diagram is for a different set of sequences.

In the left column, below the sequences, there is a Venn diagram with three circles, and numbers around it: 1101, 300, 10823, 40100, 2660, 4500, 1710, 900

And the circles are labeled "Sequence 1", "Sequence 2", "Sequence 3" — but which sequences? Perhaps the ones from the top, but they don't contain these numbers.

Another possibility: Perhaps "Sequence 1", "Sequence 2", "Sequence 3" refer to the types of sequences, like arithmetic with common difference 5, etc., but not specified.

Perhaps from the context, the sequences are defined by their rules, and we need to see which numbers fit which rule.

But it's ambiguous.

Let's look at the numbers: 1101, 300, 10823, 40100, 2660, 4500, 1710, 900

Notice that 900, 1710, 2660, 300, 4500, etc.

Perhaps they are to be sorted into the Venn diagram based on divisibility or something.

But the circles are labeled "Sequence 1", "Sequence 2", "Sequence 3", so likely related to the sequences above.

Perhaps for the Venn diagram, the sequences are the ones we have, and we need to see if the numbers are in those sequences, but as we saw, none are.

Unless we extend the sequences.

For example, Sequence 1: 6573, 6578, 6583, 6593, 6603 — if we continue, 6613, 6623, etc., not matching.

Sequence 2: 196, 1081, 1966, 1981, 1996 — next would be 2011, 2026, etc.

1081 is in it, and 10823 is given — 10823 vs 1081, not the same.

10823 might be a typo for 1081, but unlikely.

Another idea: Perhaps "Sequence 1", "Sequence 2", "Sequence 3" refer to the rules we found, and the numbers are to be checked if they can be part of such sequences.

But that's vague.

Let's calculate the differences or see if they fit arithmetic sequences.

Perhaps the Venn diagram is for the numbers to be placed based on which of the three sequences they belong to, but since the sequences are finite, we need to see if they match the pattern.

For example, for Sequence 1 rule: from start, +5, +5, +10, +10 — but that's not a single rule.

Perhaps for Sequence 1, the rule is that it increases by 5 for the first two steps, then by 10, but for classification, it's hard.

Let's look at the right column bottom: "22 240, 22 700, 23 900, ____, 26 300" — we said missing is 25100.

And "22 240" likely means 22240, etc.

Now for the left column Venn diagram, perhaps the numbers are to be placed in the regions based on whether they are in Sequence 1,2, or 3 as defined by their rules.

But let's try to see if any number fits Sequence 3 rule: +490.

Start from some point.

For example, if a number is in an arithmetic sequence with d=490.

Take 900: 900 mod 490 = 900 - 490*1 = 410, not 0.

4500 div 490 = 9*490=4410, 4500-4410=90, not 0.

1710 / 490 = 3*490=1470, 1710-1470=240, not 0.

2660 / 490 = 5*490=2450, 2660-2450=210, not 0.

300 / 490 <1, remainder 300.

1101 / 490 = 2*490=980, 1101-980=121, not 0.

10823 / 490 = let's calculate: 490*22 = 10780, 10823-10780=43, not 0.

40100 / 490 = 490*81 = 39690, 40100-39690=410, not 0.

None are divisible by 490, so not in a sequence with d=490 starting from 0.

Perhaps from the first term.

For Sequence 3, first term 18720, so numbers congruent to 18720 mod 490.

18720 div 490: 490*38 = 18620, 18720-18620=100, so 18720 ≡ 100 mod 490.

So numbers ≡ 100 mod 490.

Check the numbers:

1101 mod 490: 490*2=980, 1101-980=121 ≠100

300 mod 490 = 300 ≠100

10823 mod 490: 490*22=10780, 10823-10780=43 ≠100

40100 mod 490: 490*81=39690, 40100-39690=410 ≠100

2660 mod 490: 490*5=2450, 2660-2450=210 ≠100

4500 mod 490: 490*9=4410, 4500-4410=90 ≠100

1710 mod 490: 490*3=1470, 1710-1470=240 ≠100

900 mod 490 = 900-490=410, 410-490<0, so 410 ≠100

None match.

For Sequence 1: rule is not constant, so hard.

Perhaps the Venn diagram is for a different purpose.

Another idea: Perhaps "Sequence 1", "Sequence 2", "Sequence 3" refer to the three sequences in the left column, and the numbers are to be placed in the Venn diagram based on which sequence they could be part of if extended, but with the rule.

But for Sequence 1, if we assume the rule is +5 for first two, then +10, but for a number to be in it, it must fit the pattern from the start.

For example, for a number to be in Sequence 1, it must be 6573 +5k for k=0,1,2, then 6573 +5*2 +10m for m=1,2, etc., but messy.

Perhaps the Venn diagram is independent, and the sequences are defined by the numbers given in the diagram.

Let's read the text: "These numbers shown appear in the correct cell above or in the correct diagram. If you need to, use the clues to work out where the numbers should be placed in the cells of the diagrams."

And there is a Venn diagram with three circles, and numbers around it: 1101, 300, 10823, 40100, 2660, 4500, 1710, 900

And the circles are labeled "Sequence 1", "Sequence 2", "Sequence 3" — but no definition.

Perhaps from the context, the sequences are the ones we have, and we need to see which numbers are in which sequence by checking if they satisfy the rule.

But as above, not working.

Another thought: Perhaps "Sequence 1", "Sequence 2", "Sequence 3" refer to the rules like "increasing by 5", "increasing by 10", etc., but not specified.

Let's look at the numbers: 900, 1710, 2660, 300, 4500, 1101, 10823, 40100

Notice that 900, 1710, 2660 — differences: 1710-900=810, 2660-1710=950, not constant.

900, 4500 — 4500/900=5, so perhaps geometric.

1710/900=1.9, not 5.

Perhaps they are to be sorted by size or something.

Perhaps the Venn diagram is for the numbers to be placed based on whether they are divisible by 3, 5, etc., but the labels are "Sequence 1", etc.

I recall that in some worksheets, the Venn diagram is for classifying numbers based on which arithmetic sequences they belong