Arithmetic Sequence Worksheets - Free Printable

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Arithmetic Sequence - MCQ

1. Which of the following sequences is an arithmetic progression?
a) 3, 15, 90, 760, ...
b) –1, –10, –19, –28, ...
c) 0.2, 0.4, 0.8, 1.6, ...

2. Which of the following is not an arithmetic sequence?
a) –36, –30, –24, –12, ...
b) 3, 12, 21, 30, 39, ...
c) 21, 42, 63, 84, 105, ...

3. Which of the following sequences is an arithmetic progression?
a) 62, 64, 68, 14, ...
b) –127, –121, –115, –107, ...
c) –1, –2, –4, –8, ...

4. Which of the following sequences is not an arithmetic progression?
a) 0.1, 0.2, 0.3, 0.4, ...
b) 1/2, 1/4, 1/8, 1/16, ...
c) 1/3, 2/3, 1, 4/3, ...

5. Which of the following is an arithmetic sequence?
a) –68, –57, –46, –35, ...
b) 39, 30, 3, 21, 3, 15, ...
c) –62, –65, –68, –71, ...

6. Which of the following sequence is not an arithmetic progression?
a) 1/2, 2/3, 3/4, 4/5, ...
b) 0.24, 0.28, 0.32, 0.36, ...
c) 1/4, 1/2, 3/4, 1, ...

7. Which of the following is an arithmetic sequence?
a) 63, 30, 3, 14, 100, 5, ...
b) 6, 9, 12, 18, 24, ...
c) 27, 25, 23, 21, ...

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Let me now solve each question one by one, explaining the reasoning.

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✔ Understanding Arithmetic Sequences

An arithmetic sequence has a constant difference between consecutive terms. That is:
> $ a_{n+1} - a_n = d $ (common difference)

If this difference is not constant, it's not an arithmetic sequence.

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Question 1: Which is an arithmetic progression?

a) 3, 15, 90, 760, ...
→ Differences: 15–3=12, 90–15=75, 760–90=670 → Not constant → ✘

b) –1, –10, –19, –28, ...
→ Differences: –10 – (–1) = –9; –19 – (–10) = –9; –28 – (–19) = –9 → Constant (d = –9) → ✔

c) 0.2, 0.4, 0.8, 1.6, ...
→ 0.4–0.2=0.2; 0.8–0.4=0.4; 1.6–0.8=0.8 → Not constant → ✘

✔ Answer: b)

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Question 2: Which is NOT an arithmetic sequence?

a) –36, –30, –24, –12, ...
→ –30 – (–36) = 6; –24 – (–30) = 6; –12 – (–24) = 12 → Wait! Last difference is 12 ≠ 6 → Not constant → ✘

Wait — let's double-check:
–36, –30, –24, –12 → differences: +6, +6, +12 → So not arithmetic?

But wait — maybe typo? Let’s assume the sequence is meant to be decreasing by 6:
–36, –30, –24, –18, –12 → then yes, d = 6. But as written, it jumps from –24 to –12 → difference of +12 → not consistent.

So if the sequence is: –36, –30, –24, –12 → then not arithmetic.

But let’s check others.

b) 3, 12, 21, 30, 39 → differences: 9, 9, 9, 9 → d = 9 → ✔

c) 21, 42, 63, 84, 105 → differences: 21, 21, 21, 21 → d = 21 → ✔

So only a) fails.

✔ Answer: a)

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Question 3: Which is an arithmetic progression?

a) 62, 64, 68, 14, ...
→ 64–62=2; 68–64=4; 14–68=–54 → Not constant → ✘

b) –127, –121, –115, –107, ...
→ –121 – (–127) = 6; –115 – (–121) = 6; –107 – (–115) = 8 → Wait: 6, 6, 8 → not constant → ✘

Wait — last term is –107? From –115 to –107 is +8, but previous was +6 → not arithmetic.

Is there a typo? Maybe should be –109? But as written → not arithmetic.

c) –1, –2, –4, –8, ...
→ –2 – (–1) = –1; –4 – (–2) = –2; –8 – (–4) = –4 → differences: –1, –2, –4 → not constant → ✘

All seem invalid?

Wait — perhaps b) has a typo. Let’s recheck:

–127, –121, –115, –107 →
–121 – (–127) = 6
–115 – (–121) = 6
–107 – (–115) = 8 → not 6 → so no.

But maybe it’s supposed to be –109? Then it would be d=6.

As written → none are arithmetic?

But that can’t be.

Wait — maybe b) is: –127, –121, –115, –109 → then d=6 → arithmetic.

But it says –107 → so likely a typo.

Alternatively, maybe none are correct?

But let’s assume it's printed correctly.

Wait — could a) be: 62, 64, 68, 72? But it says 14 → no.

Maybe b) is intended to be: –127, –121, –115, –109 → d=6 → arithmetic.

But as written: –107 → difference of +8 → breaks pattern.

So unless typo, no valid arithmetic sequence?

But we must pick one.

Wait — maybe b) is: –127, –121, –115, –107 → let's compute:

-127 → -121 → +6
-121 → -115 → +6
-115 → -107 → +8 → not same → so not arithmetic.

So all three fail?

That seems odd.

Wait — c): –1, –2, –4, –8 → geometric, not arithmetic.

So perhaps none are arithmetic?

But that contradicts the format.

Wait — maybe b) is: –127, –121, –115, –109 → but it says –107.

Alternatively, maybe a): 62, 64, 68, 14 → clearly not.

Unless it's a typo: 62, 64, 68, 72 → then d=2, 4, 4 → still not constant.

No.

Wait — perhaps b) is correct if we ignore the last term? No.

Maybe I misread.

Let me recheck:
b) –127, –121, –115, –107

Differences:
-121 - (-127) = 6
-115 - (-121) = 6
-107 - (-115) = 8 → not 6 → so not arithmetic.

So none are arithmetic?

But that can't be.

Wait — maybe a): 62, 64, 68, 14 → no.

Perhaps c) is meant to be: –1, –2, –3, –4 → but it’s –1, –2, –4, –8 → geometric.

So maybe none are arithmetic?

But the question asks “which is”, implying one is.

Wait — perhaps b) is: –127, –121, –115, –109 → but it says –107 → typo.

Alternatively, maybe the sequence is: –127, –121, –115, –109 → then d=6 → arithmetic.

But since it says –107, we must go with that.

So none?

But let's move on and come back.

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Question 4: Which is NOT an arithmetic progression?

a) 0.1, 0.2, 0.3, 0.4 → differences: 0.1, 0.1, 0.1 → d=0.1 → ✔ arithmetic

b) 1/2, 1/4, 1/8, 1/16 → halves → geometric → differences:
1/4 – 1/2 = –1/4; 1/8 – 1/4 = –1/8; etc. → not constant → ✘ not arithmetic

c) 1/3, 2/3, 1, 4/3 →
2/3 – 1/3 = 1/3
1 – 2/3 = 1/3
4/3 – 1 = 1/3 → d = 1/3 → ✔ arithmetic

So b) is not arithmetic.

✔ Answer: b)

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Question 5: Which is an arithmetic sequence?

a) –68, –57, –46, –35 →
–57 – (–68) = 11
–46 – (–57) = 11
–35 – (–46) = 11 → d = 11 → ✔

b) 39, 30, 3, 21, 3, 15 →
30–39=–9; 3–30=–27; 21–3=18; 3–21=–18; 15–3=12 → not constant → ✘

c) –62, –65, –68, –71 →
–65 – (–62) = –3; –68 – (–65) = –3; –71 – (–68) = –3 → d = –3 → ✔

So both a and c are arithmetic.

But the question says “which” — implying one answer.

But a and c both work.

Wait — let’s check b) again: 39, 30, 3, 21, 3, 15

This seems jumbled — possibly typo.

But a and c both are arithmetic.

But since it’s multiple choice with single answer, likely a is intended.

But c also works.

Wait — maybe b) is: 39, 30, 21, 12, 3 → then d=–9 → arithmetic.

But as written: 39, 30, 3, 21, 3, 15 → not.

So a and c are both arithmetic.

But if only one is allowed, perhaps a is correct.

But c is also.

Wait — maybe the question allows only one correct choice.

But both are correct.

Possibly a is listed first.

But let’s proceed.

Assuming the answer is a or c.

But c: –62, –65, –68, –71 → yes, d=–3 → ✔

So both are valid.

But perhaps the test expects a.

Wait — maybe b) is meant to be: 39, 30, 21, 12, 3 → d=–9 → arithmetic.

But as written → not.

So a and c are correct.

But since only one choice, maybe it's a.

But let’s look at Question 6.

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Question 6: Which is NOT an arithmetic progression?

a) 1/2, 2/3, 3/4, 4/5 →
2/3 – 1/2 = (4–3)/6 = 1/6
3/4 – 2/3 = (9–8)/12 = 1/12 → not equal → not arithmetic → ✘

b) 0.24, 0.28, 0.32, 0.36 →
0.28–0.24=0.04; 0.32–0.28=0.04; 0.36–0.32=0.04 → d=0.04 → ✔

c) 1/4, 1/2, 3/4, 1 →
1/2 – 1/4 = 1/4; 3/4 – 1/2 = 1/4; 1 – 3/4 = 1/4 → d=1/4 → ✔

So only a) is not arithmetic.

✔ Answer: a)

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Question 7: Which is an arithmetic sequence?

a) 63, 30, 3, 14, 100, 5 →
30–63=–33; 3–30=–27; 14–3=11; 100–14=86; 5–100=–95 → not constant → ✘

b) 6, 9, 12, 18, 24 →
9–6=3; 12–9=3; 18–12=6; 24–18=6 → differences: 3,3,6,6 → not constant → ✘

c) 27, 25, 23, 21, ... →
25–27=–2; 23–25=–2; 21–23=–2 → d=–2 → ✔

✔ Answer: c)

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Summary of Answers:

| Q | Answer |
|---|--------|
| 1 | b |
| 2 | a |
| 3 | ? (possibly typo) |
| 4 | b |
| 5 | a or c (both valid) |
| 6 | a |
| 7 | c |

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Revisit Question 3:

Given:
a) 62, 64, 68, 14 → differences: +2, +4, –54 → no
b) –127, –121, –115, –107 → +6, +6, +8 → not constant → no
c) –1, –2, –4, –8 → –1, –2, –4 → not constant → no

None are arithmetic?

But that can't be.

Wait — maybe b) is: –127, –121, –115, –109 → then d=6 → yes.

Or perhaps a) is: 62, 64, 66, 68 → then d=2 → yes.

But as written, none are.

But perhaps b) is intended to be: –127, –121, –115, –109 → then it's arithmetic.

Alternatively, maybe a): 62, 64, 68, 72 → then d=2,4,4 → not constant.

Still no.

Wait — b): –127, –121, –115, –107 →
From –115 to –107 is +8, but earlier +6 → not arithmetic.

So unless typo, no correct option.

But perhaps the sequence is: –127, –121, –115, –109 → then it is.

So likely b) is intended to be correct.

Assume b) is correct due to typo.

So answer: b)

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Final Answers:

1. b
2. a
3. b (assuming typo: –109 instead of –107)
4. b
5. a (or c) — both work, but a is listed first
6. a
7. c

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If you can confirm the exact values in the image (especially for Q3 and Q5), I can refine further.

But based on standard interpretation and likely typos, here’s the best guess:

✔ Final Answer Key:

1. b
2. a
3. b
4. b
5. a
6. a
7. c

Let me know if you'd like explanations for any specific question or if you have the image with clearer numbers!