Students look at the sequence of numbers and shapes to determine the missing item in the pattern.

Let's solve each pattern step by step. The goal is to identify the repeating sequence and determine what comes last in each row.

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Problem 1:

Sequence:
5 ● 7 5 ● ____

Look at the pattern:
- Numbers: 5, 7, 5 → repeats? Let's see.
- Symbols: ● appears after 5, then 7, then 5 again, then ● again.

So let’s break it down:
- Position 1: 5
- Position 2: ●
- Position 3: 7
- Position 4: 5
- Position 5: ●
- Position 6: ?

We can see a possible repeating unit: 5 ● 7, then 5 ●, so maybe the pattern is:
5 ● 7, then repeat?

But wait — we have:
5 ● 7 5 ● ___

Wait — perhaps the pattern is alternating between numbers and shapes, but let's look more closely.

Alternatively, consider that the number pattern might be:
5, 7, 5, 7...? But here it's 5, 7, 5, so maybe not.

Wait — look again:

Positions:
1. 5
2. ● (shape)
3. 7
4. 5
5. ●
6. ?

Now notice:
- The number 5 appears at positions 1, 4
- Then 7 at position 3
- So maybe the numbers go: 5, 7, 5, 7...?
But we have: 5, 7, 5 → then next should be 7

And the shape ● appears at positions 2 and 5 → every 3rd item?

Wait — let’s list with positions:

| Pos | Item |
|-----|------|
| 1 | 5 |
| 2 | ● |
| 3 | 7 |
| 4 | 5 |
| 5 | ● |
| 6 | ? |

Now check if there’s a repeating pattern of three items:
(5, ●, 7), then (5, ●, ?)

But after (5, ●, 7), we have (5, ●, ?)

That doesn’t match.

Wait — perhaps the pattern is: 5, ●, 7, 5, ●, 7 — so it repeats every three?

But 5 ● 7, then 5 ● 7 → yes!

But here we have:
5 ● 7 5 ● ____

So:
- First group: 5 ● 7
- Second group: 5 ● ?

So maybe it's not repeating every 3, because second group starts with 5 again, but first was 5, then ●, then 7.

Wait — actually, let's try this:

Maybe the pattern is alternating between numbers and shapes, and the numbers alternate between 5 and 7.

Let’s look at just the numbers:
- Positions 1: 5
- Position 3: 7
- Position 4: 5
- So maybe: 5, 7, 5, 7,...

So far: 5, 7, 5 → so next number should be 7

Now, shapes:
- Position 2: ●
- Position 5: ●
- So ● appears every 3rd item? Positions 2 and 5 → difference of 3.

So shape at positions 2, 5 → next would be position 8, but we only need position 6.

But position 6 is after ● at position 5.

So what comes after ●?

In the first cycle: 5, ●, 7 → so ● is followed by 7.

Then: 5, ●, ? → so likely 7

So the full pattern seems to be:
5, ●, 7, 5, ●, 7

Yes! That makes sense.

So the last item should be 7

✔ Answer for #1: 7

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Problem 2:

Sequence:
3 ▲ 1 ◎ 3 ____

Break it down:

| Pos | Item |
|-----|------|
| 1 | 3 |
| 2 | ▲ |
| 3 | 1 |
| 4 | ◎ |
| 5 | 3 |
| 6 | ? |

Now look for a pattern.

Numbers: 3, 1, 3 → so maybe alternating between 3 and 1?

But: 3, 1, 3 → so next could be 1

Shapes: ▲ at pos 2, ◎ at pos 4 → both are symbols.

Now check:
Pos 1: 3
Pos 2: ▲
Pos 3: 1
Pos 4: ◎
Pos 5: 3
Pos 6: ?

So maybe the pattern is: 3, ▲, 1, ◎, 3, ?

Notice:
- After 3 → ▲
- After ▲ → 1
- After 1 → ◎
- After ◎ → 3
- After 3 → ?

But from earlier: 3 → ▲ → 1 → ◎ → 3 → ?

So now we’re back to 3, which was the start.

So maybe the pattern repeats every 4 items?

Let’s test:

Group 1: 3, ▲, 1, ◎
Group 2: 3, ?, ...

Wait — but we have:
3, ▲, 1, ◎, 3, ?

So maybe the pattern is 3, ▲, 1, ◎, then repeats?

But after ◎ comes 3 — which is same as first number.

So maybe it’s a repeating block: 3, ▲, 1, ◎, then again 3, ▲, 1, ◎...

But here we have:
3, ▲, 1, ◎, 3, ?

So after ◎ comes 3 — which matches the start.

Then next should be ▲ (same as after 3).

So the pattern is:
- 3 → ▲
- ▲ → 1
- 1 → ◎
- ◎ → 3
- 3 → ▲

So after 3, comes ▲.

Thus, the missing item is ▲

✔ Answer for #2: ▲

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Problem 3:

Sequence:
6 ★ ○ 4 6 ____

Break it down:

| Pos | Item |
|-----|------|
| 1 | 6 |
| 2 | ★ |
| 3 | ○ |
| 4 | 4 |
| 5 | 6 |
| 6 | ? |

Numbers: 6, 4, 6 → so maybe alternating between 6 and 4?

But 6, 4, 6 → next should be 4

Shapes: ★ at pos 2, ○ at pos 3

Now look at the structure:

6, ★, ○, 4, 6, ?

So perhaps the pattern is:
- 6, ★, ○, 4, then 6, ?

But what follows 6?

Earlier: after 6 → ★ → ○ → 4 → 6 → ?

So maybe the pattern is: 6, ★, ○, 4, then repeat?

But then after 4 comes 6 — which matches.

Then after 6, should come ★ again?

But let’s see if it's two parts:

Maybe it's two alternating sequences?

Or perhaps the pattern is: 6, ★, ○, 4, then 6, ★, ...

But we have: 6, ★, ○, 4, 6, ?

So after 4 comes 6 — same as first number.

Then next should be ★ (same as after first 6)

So:
6 → ★
★ → ○
○ → 4
4 → 6
6 → ★

So the pattern is 6, ★, ○, 4, then repeat?

But wait: 6, ★, ○, 4, 6 → then next should be ★

Yes.

So missing item is ★

✔ Answer for #3: ★

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Problem 4:

Sequence:
◎ ● 2 ■ ◎ ____

Break it down:

| Pos | Item |
|-----|------|
| 1 | ◎ |
| 2 | ● |
| 3 | 2 |
| 4 | ■ |
| 5 | ◎ |
| 6 | ? |

Now look:

Items: ◎, ●, 2, ■, ◎, ?

We see ◎ at pos 1 and 5 — every 4th item?

Pattern:
◎ → ● → 2 → ■ → ◎ → ?

So maybe the pattern is: ◎, ●, 2, ■, then repeat?

Then after ◎ comes ●

So next item should be ●

Check:
1. ◎
2. ●
3. 2
4. ■
5. ◎ → same as pos 1
6. ? → should be same as pos 2 → ●

Yes.

So the pattern is repeating every 4 items: ◎, ●, 2, ■

So after ◎ (pos 5), comes ● (pos 6)

✔ Answer for #4: ●

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✔ Final Answers:

1. 7
2. ▲
3. ★
4. ●

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Summary:

| Problem | Answer |
|--------|--------|
| 1 | 7 |
| 2 | ▲ |
| 3 | ★ |
| 4 | ● |

These follow repeating patterns based on alternating numbers and shapes.