Solved ARITHMETIC SEQUENCES & SERIES WORKSHEET (1) Q1. | Chegg.com - Free Printable

Let’s go through each sequence one by one to check if it’s arithmetic.
An arithmetic sequence has a constant difference between consecutive terms — that means you add (or subtract) the same number every time to get the next term.

We’ll check the difference between each pair of terms. If the difference is always the same, then it’s arithmetic, and we can find the next three terms by adding that common difference again and again.

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1. 17, 12, 7, 2, ...

Check differences:
12 - 17 = -5
7 - 12 = -5
2 - 7 = -5 → Constant! So yes, arithmetic with d = -5.

Next three terms:
2 + (-5) = -3
-3 + (-5) = -8
-8 + (-5) = -13

✔ Arithmetic. Next terms: -3, -8, -13

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2. -129, -98, -67, ...

Differences:
-98 - (-129) = -98 + 129 = 31
-67 - (-98) = -67 + 98 = 31 → Constant! So yes, arithmetic with d = 31.

Next three terms:
-67 + 31 = -36
-36 + 31 = -5
-5 + 31 = 26

✔ Arithmetic. Next terms: -36, -5, 26

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3. 1/4, 2/6, 3/8, 4/10, ...

First, simplify fractions to make comparison easier:
1/4 = 0.25
2/6 = 1/3 ≈ 0.333...
3/8 = 0.375
4/10 = 0.4

Now check differences:
0.333 - 0.25 = ~0.083
0.375 - 0.333 = ~0.042 → Not the same!

Wait — maybe look at numerators and denominators separately?
Numerators: 1, 2, 3, 4 → increasing by 1
Denominators: 4, 6, 8, 10 → increasing by 2

But the actual values are not changing by a constant amount. Let’s compute exact differences:

Term 2 - Term 1: 2/6 - 1/4 = (4/12 - 3/12) = 1/12
Term 3 - Term 2: 3/8 - 2/6 = 3/8 - 1/3 = (9/24 - 8/24) = 1/24
→ 1/12 ≠ 1/24 → NOT constant.

✘ Not arithmetic.

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4. 12, 24, 36, 48, ...

Differences:
24 - 12 = 12
36 - 24 = 12
48 - 36 = 12 → Constant! So yes, arithmetic with d = 12.

Next three terms:
48 + 12 = 60
60 + 12 = 72
72 + 12 = 84

✔ Arithmetic. Next terms: 60, 72, 84

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5. 36k, 49k, 64k, 81k, ...

Assuming k is a constant (like a variable or multiplier), let’s ignore k for now and look at coefficients:
36, 49, 64, 81 → These are perfect squares: 6², 7², 8², 9²

Differences:
49 - 36 = 13
64 - 49 = 15
81 - 64 = 17 → Increasing by 2 each time → NOT constant.

So even though they follow a pattern, the difference isn’t constant → ✘ Not arithmetic.

*(Note: This is actually a quadratic sequence, not arithmetic.)*

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6. 3, -6, 12, -24, ...

Differences:
-6 - 3 = -9
12 - (-6) = 18
-24 - 12 = -36 → Differences: -9, 18, -36 → Not constant.

Also, notice: each term is multiplied by -2 → geometric, not arithmetic.

✘ Not arithmetic.

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7. -29, -2, 25, ...

Differences:
-2 - (-29) = -2 + 29 = 27
25 - (-2) = 25 + 2 = 27 → Constant! So yes, arithmetic with d = 27.

Next three terms:
25 + 27 = 52
52 + 27 = 79
79 + 27 = 106

✔ Arithmetic. Next terms: 52, 79, 106

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8. -4.5, -9.5, -14.5, ...

Differences:
-9.5 - (-4.5) = -9.5 + 4.5 = -5
-14.5 - (-9.5) = -14.5 + 9.5 = -5 → Constant! So yes, arithmetic with d = -5.

Next three terms:
-14.5 + (-5) = -19.5
-19.5 + (-5) = -24.5
-24.5 + (-5) = -29.5

✔ Arithmetic. Next terms: -19.5, -24.5, -29.5

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9. 7, -3.5, -14, ...

Differences:
-3.5 - 7 = -10.5
-14 - (-3.5) = -14 + 3.5 = -10.5 → Constant! So yes, arithmetic with d = -10.5.

Next three terms:
-14 + (-10.5) = -24.5
-24.5 + (-10.5) = -35
-35 + (-10.5) = -45.5

✔ Arithmetic. Next terms: -24.5, -35, -45.5

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10. 8, -2, 1/2, ...

Convert to decimals or fractions to compare:

8, -2, 0.5

Differences:
-2 - 8 = -10
0.5 - (-2) = 0.5 + 2 = 2.5 → -10 ≠ 2.5 → Not constant.

Also, check ratios:
-2 / 8 = -0.25
0.5 / (-2) = -0.25 → Oh! It’s geometric with ratio -1/4.

But question asks for arithmetic → ✘ Not arithmetic.

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Final Answer:

1. Yes; next terms: -3, -8, -13
2. Yes; next terms: -36, -5, 26
3. No
4. Yes; next terms: 60, 72, 84
5. No
6. No
7. Yes; next terms: 52, 79, 106
8. Yes; next terms: -19.5, -24.5, -29.5
9. Yes; next terms: -24.5, -35, -45.5
10. No