Sequence and Series Worksheets - Free Printable

I'll work through each sequence to determine if it's arithmetic and find the next three terms where applicable.

What is an arithmetic sequence?
An arithmetic sequence has a constant difference between consecutive terms. I need to check if subtracting each term from the next gives the same number (called the common difference, d).

Let me analyze each sequence:

1. 17, 12, 7, 2, ...
- 12 - 17 = -5
- 7 - 12 = -5
- 2 - 7 = -5
✓ This IS arithmetic with d = -5
Next three terms: 2 + (-5) = -3, -3 + (-5) = -8, -8 + (-5) = -13

2. -129, -98, -67, ...
- (-98) - (-129) = -98 + 129 = 31
- (-67) - (-98) = -67 + 98 = 31
✓ This IS arithmetic with d = 31
Next three terms: -67 + 31 = -36, -36 + 31 = -5, -5 + 31 = 26

3. 1/4, 2/6, 3/8, 4/10, ...
Let me simplify these fractions first:
- 1/4 = 0.25
- 2/6 = 1/3 ≈ 0.333...
- 3/8 = 0.375
- 4/10 = 2/5 = 0.4

Checking differences:
- 1/3 - 1/4 = 4/12 - 3/12 = 1/12
- 3/8 - 1/3 = 9/24 - 8/24 = 1/24
- 2/5 - 3/8 = 16/40 - 15/40 = 1/40

The differences are NOT the same (1/12 ≠ 1/24 ≠ 1/40)
✗ This is NOT arithmetic

4. 12, 24, 36, 48, ...
- 24 - 12 = 12
- 36 - 24 = 12
- 48 - 36 = 12
✓ This IS arithmetic with d = 12
Next three terms: 48 + 12 = 60, 60 + 12 = 72, 72 + 12 = 84

5. 36k, 49k, 64k, 81k, ...
- 49k - 36k = 13k
- 64k - 49k = 15k
- 81k - 64k = 17k

The differences are NOT the same (13k ≠ 15k ≠ 17k)
✗ This is NOT arithmetic

6. 3, -6, 12, -24, ...
- (-6) - 3 = -9
- 12 - (-6) = 18
- (-24) - 12 = -36

The differences are NOT the same (-9 ≠ 18 ≠ -36)
✗ This is NOT arithmetic (this appears to be geometric instead)

7. -29, -2, 25, ...
- (-2) - (-29) = -2 + 29 = 27
- 25 - (-2) = 25 + 2 = 27
✓ This IS arithmetic with d = 27
Next three terms: 25 + 27 = 52, 52 + 27 = 79, 79 + 27 = 106

8. -4.5, -9.5, -14.5, ...
- (-9.5) - (-4.5) = -9.5 + 4.5 = -5
- (-14.5) - (-9.5) = -14.5 + 9.5 = -5
✓ This IS arithmetic with d = -5
Next three terms: -14.5 + (-5) = -19.5, -19.5 + (-5) = -24.5, -24.5 + (-5) = -29.5

9. 7, -3.5, -14, ...
- (-3.5) - 7 = -10.5
- (-14) - (-3.5) = -14 + 3.5 = -10.5
✓ This IS arithmetic with d = -10.5
Next three terms: -14 + (-10.5) = -24.5, -24.5 + (-10.5) = -35, -35 + (-10.5) = -45.5

10. 8, -2, 1/2, ...
- (-2) - 8 = -10
- 1/2 - (-2) = 0.5 + 2 = 2.5

The differences are NOT the same (-10 ≠ 2.5)
✗ This is NOT arithmetic

Final Answer:
1. Yes, arithmetic. Next three terms: -3, -8, -13
2. Yes, arithmetic. Next three terms: -36, -5, 26
3. No, not arithmetic
4. Yes, arithmetic. Next three terms: 60, 72, 84
5. No, not arithmetic
6. No, not arithmetic
7. Yes, arithmetic. Next three terms: 52, 79, 106
8. Yes, arithmetic. Next three terms: -19.5, -24.5, -29.5
9. Yes, arithmetic. Next three terms: -24.5, -35, -45.5
10. No, not arithmetic