Arithmetic Sequence Worksheet Answer Key with solutions for finding the next three terms and common differences.

The image you've uploaded is a completed Arithmetic Sequence Math Worksheet with an answer key. The task is to find the next three terms and the common difference for each given arithmetic sequence.

Let’s go through each sequence, verify the answers, and explain how to solve them step by step.

---

🔷 What is an Arithmetic Sequence?

An arithmetic sequence is a list of numbers where each term after the first is obtained by adding a constant called the common difference (d).

To find:
- Next terms: Add the common difference repeatedly.
- Common difference: Subtract any term from the next term:
$ d = a_{n+1} - a_n $

---

✔ Problem 1: 12, 24, 36, 48, 60, __, __, __

- Find common difference:
$ 24 - 12 = 12 $ → $ d = 12 $
- Next terms:
$ 60 + 12 = 72 $,
$ 72 + 12 = 84 $,
$ 84 + 12 = 96 $
- ✔ Answer: 72, 84, 96, common difference = 12

---

✔ Problem 2: 3, 0, -3, -6, -9, __, __, __

- $ 0 - 3 = -3 $ → $ d = -3 $
- Next terms:
$ -9 + (-3) = -12 $,
$ -12 + (-3) = -15 $,
$ -15 + (-3) = -18 $
- ✔ Answer: -12, -15, -18, common difference = -3

---

✔ Problem 3: -15, -10, -5, 0, 5, __, __, __

- $ -10 - (-15) = 5 $ → $ d = 5 $
- Next terms:
$ 5 + 5 = 10 $,
$ 10 + 5 = 15 $,
$ 15 + 5 = 20 $
- ✔ Answer: 10, 15, 20, common difference = 5

---

✔ Problem 4: 4.2, 4.5, 4.8, 5.1, 5.4, __, __, __

- $ 4.5 - 4.2 = 0.3 $ → $ d = 0.3 $
- Next terms:
$ 5.4 + 0.3 = 5.7 $,
$ 5.7 + 0.3 = 6.0 $,
$ 6.0 + 0.3 = 6.3 $
- ✔ Answer: 5.7, 6.0, 6.3, common difference = 0.3

> Note: The answer key writes "6" instead of "6.0", but both are correct since 6 = 6.0

---

✔ Problem 5: 101, 159, 217, 275, 333, __, __, __

- $ 159 - 101 = 58 $ → $ d = 58 $
- Next terms:
$ 333 + 58 = 391 $? Wait — let's check the answer key says 449, 507, 565

Wait! That doesn't match.

Let’s double-check:

- $ 159 - 101 = 58 $
- $ 217 - 159 = 58 $
- $ 275 - 217 = 58 $
- $ 333 - 275 = 58 $

So yes, $ d = 58 $

Then:
- $ 333 + 58 = 391 $
- $ 391 + 58 = 449 $
- $ 449 + 58 = 507 $
- $ 507 + 58 = 565 $

Ah! So the next three terms are 391, 449, 507, but the worksheet shows 449, 507, 565 — which are the second, third, and fourth next terms.

But the question asks for the next three terms after 333.

So the correct next three terms should be: 391, 449, 507

But the answer key says: 449, 507, 565 — this is wrong.

Wait — let’s recheck the sequence:

Sequence: 101, 159, 217, 275, 333, __, __, __

- 101 + 58 = 159
- 159 + 58 = 217
- 217 + 58 = 275
- 275 + 58 = 333
- 333 + 58 = 391
- 391 + 58 = 449
- 449 + 58 = 507

So the next three terms after 333 are: 391, 449, 507

But the answer key says: 449, 507, 565

That skips 391. So it's incorrect.

However, the common difference is correct: 58

But the first term in the answer is wrong.

✔ Corrected Answer: 391, 449, 507, common difference = 58

But the answer key has 449, 507, 565 — which is off by one term.

This might be a typo or misalignment.

Wait — perhaps the sequence was written incorrectly?

Let me re-express:

Given: 101, 159, 217, 275, 333

Check differences:
- 159 - 101 = 58
- 217 - 159 = 58
- 275 - 217 = 58
- 333 - 275 = 58

Yes, all correct.

So next:
- 333 + 58 = 391
- 391 + 58 = 449
- 449 + 58 = 507

So the next three terms are 391, 449, 507

But the answer key says 449, 507, 565 — that’s missing 391.

So either:
- The answer key is wrong, or
- The sequence was meant to skip something

But no — the pattern is clear.

✘ Error in Answer Key: Should be 391, 449, 507, not 449, 507, 565

But wait — look at the box: it says “449, 507, 565” — so the answer key is incorrect here.

Let’s continue.

---

✔ Problem 6: -50.2, -29.6, -9, 11.6, 32.2, __, __, __

- $ -29.6 - (-50.2) = 20.6 $
- $ -9 - (-29.6) = 20.6 $
- $ 11.6 - (-9) = 20.6 $
- $ 32.2 - 11.6 = 20.6 $
→ $ d = 20.6 $

Next terms:
- $ 32.2 + 20.6 = 52.8 $
- $ 52.8 + 20.6 = 73.4 $
- $ 73.4 + 20.6 = 94 $

✔ Answer: 52.8, 73.4, 94, common difference = 20.6 → ✔️ Correct

---

✔ Problem 7: -784, -725, -666, -607, -548, __, __, __

- $ -725 - (-784) = 59 $
- $ -666 - (-725) = 59 $
- $ -607 - (-666) = 59 $
- $ -548 - (-607) = 59 $
→ $ d = 59 $

Next terms:
- $ -548 + 59 = -489 $
- $ -489 + 59 = -430 $
- $ -430 + 59 = -371 $

✔ Answer: -489, -430, -371, common difference = 59 → ✔️ Correct

---

✔ Problem 8: 125, 83, 41, -1, -43, __, __, __

- $ 83 - 125 = -42 $
- $ 41 - 83 = -42 $
- $ -1 - 41 = -42 $
- $ -43 - (-1) = -42 $
→ $ d = -42 $

Next terms:
- $ -43 + (-42) = -85 $
- $ -85 + (-42) = -127 $
- $ -127 + (-42) = -169 $

✔ Answer: -85, -127, -169, common difference = -42 → ✔️ Correct

---

✘ Summary of Errors

Only Problem 5 has an error in the answer key.

#### Problem 5:
- Sequence: 101, 159, 217, 275, 333, __, __, __
- Common difference: 58 ✔
- Correct next three terms: 391, 449, 507
- But answer key says: 449, 507, 565 ✘

This is likely a typo — maybe they skipped the first term by mistake.

---

✔ Final Corrected Answers:

| Sequence | Next Three Terms | Common Difference |
|--------|------------------|-------------------|
| 12, 24, 36, 48, 60 | 72, 84, 96 | 12 |
| 3, 0, -3, -6, -9 | -12, -15, -18 | -3 |
| -15, -10, -5, 0, 5 | 10, 15, 20 | 5 |
| 4.2, 4.5, 4.8, 5.1, 5.4 | 5.7, 6.0, 6.3 | 0.3 |
| 101, 159, 217, 275, 333 | 391, 449, 507 | 58 |
| -50.2, -29.6, -9, 11.6, 32.2 | 52.8, 73.4, 94 | 20.6 |
| -784, -725, -666, -607, -548 | -489, -430, -371 | 59 |
| 125, 83, 41, -1, -43 | -85, -127, -169 | -42 |

---

✔ Conclusion

The only error is in Problem 5, where the answer key lists 449, 507, 565 as the next three terms, but the correct ones are 391, 449, 507.

All other answers are correct.

✔ How to Solve Any Arithmetic Sequence:
1. Find the common difference $ d = a_2 - a_1 $
2. Add $ d $ repeatedly to get the next terms.

Let me know if you'd like a printable version or explanation in another format!