This answer key displays the solutions for finding the next three terms and the common difference in a series of arithmetic sequences.

Since both ExplainAnswer and TeachTopic are false, we skip those sections.

Also, GeneratePractice is false, so we omit that too.

We only need to provide the Final Answer, which should be the completed worksheet with all next three terms and common differences filled in — as shown in the image.

But since the image already contains the correct answers (it’s labeled “ANSWER KEY”), and our job is to solve the problem accurately based on the task, we simply reproduce the correct answers as they appear in the key — because they are mathematically accurate.

Let’s verify one or two quickly to be sure:

1. Sequence: 12, 24, 36, 48, 60 → difference = 12 → next: 72, 84, 96 ✔
2. Sequence: 3, 0, -3, -6, -9 → difference = -3 → next: -12, -15, -18 ✔
3. Sequence: -15, -10, -5, 0, 5 → difference = 5 → next: 10, 15, 20 ✔
4. Sequence: 4.2, 4.5, 4.8, 5.1, 5.4 → difference = 0.3 → next: 5.7, 6.0, 6.3 ✔
5. Sequence: 101, 159, 217, 275, 333 → difference = 58 → next: 391? Wait — 333 + 58 = 391, but image says 449? Let’s check:
159 - 101 = 58
217 - 159 = 58
275 - 217 = 58
333 - 275 = 58 → so next should be 333 + 58 = 391, then 449, then 507? But image shows: 449, 507, 565 — that’s wrong!
Wait — 333 + 58 = 391, not 449. So image has error? Or did I misread?

Wait — let me recalculate:

101
+58 → 159
+58 → 217
+58 → 275
+58 → 333
+58 → 391
+58 → 449
+58 → 507
+58 → 565

Ah! The sequence given is: 101, 159, 217, 275, 333 — that’s 5 terms. Next three should be 391, 449, 507? But image says 449, 507, 565 — that skips 391.

Wait — maybe the sequence starts at term 1:
Term 1: 101
Term 2: 159
Term 3: 217
Term 4: 275
Term 5: 333
Then term 6: 391
Term 7: 449
Term 8: 507
Term 9: 565

But the problem says “find the next three terms” after 333 — so it should be 391, 449, 507.

But the answer key says 449, 507, 565 — which would be terms 7, 8, 9 — skipping term 6.

That’s a mistake in the answer key? Or perhaps I miscounted.

Wait — let’s list them with positions:

Position 1: 101
Position 2: 159
Position 3: 217
Position 4: 275
Position 5: 333
→ Next three: position 6, 7, 8 → 391, 449, 507

But the image shows: 449, 507, 565 — which is positions 7, 8, 9.

That’s incorrect.

Similarly, for the decimal one: 4.2, 4.5, 4.8, 5.1, 5.4 → next should be 5.7, 6.0, 6.3 — image has that correct.

For negative decimals: -50.2, -29.6, -9, 11.6, 32.2 → difference = 20.6 → next: 52.8, 73.4, 94.0 — image has that.

For large negatives: -784, -725, -666, -607, -548 → difference = 59 → next: -489, -430, -371 — image has that.

Last one: 125, 83, 41, -1, -43 → difference = -42 → next: -85, -127, -169 — image has that.

So only the fifth sequence seems off.

Wait — let’s double-check the fifth sequence:

101, 159, 217, 275, 333

Differences:
159 - 101 = 58
217 - 159 = 58
275 - 217 = 58
333 - 275 = 58 → correct.

Next term: 333 + 58 = 391
Then 391 + 58 = 449
Then 449 + 58 = 507

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

But the image says: 449, 507, 565 — which is wrong.

However, since this is an "answer key" image provided by the user, and our instruction is to solve the problem accurately, we must correct it.

But wait — perhaps the problem is to find the next three terms *after* the last given term, and the answer key is correct? No, 333 + 58 = 391, not 449.

Unless... is 333 not the fifth term? Let's count:

Given: 101, 159, 217, 275, 333 — that's five numbers.

The next three are the sixth, seventh, eighth.

Sixth: 333 + 58 = 391
Seventh: 391 + 58 = 449
Eighth: 449 + 58 = 507

So the answer key has a typo — it should be 391, 449, 507, not 449, 507, 565.

But 565 - 507 = 58, so if they meant to start from 449, that would be wrong.

Perhaps the sequence is indexed differently? Unlikely.

Another possibility: maybe the common difference is calculated incorrectly? But 159-101=58, etc., all good.

I think the answer key has an error in that row.

But since the user provided the image as "ANSWER KEY", and our task is to solve the problem accurately, we should provide the correct mathematical answer.

However, the instruction says: "Solve the problem accurately." and "verify your answer before writing it in the Final Answer section."

So for accuracy, we must correct the error.

But let's check the other sequences again to be thorough.

First sequence: 12,24,36,48,60 → diff 12 → next 72,84,96 — correct.

Second: 3,0,-3,-6,-9 → diff -3 → next -12,-15,-18 — correct.

Third: -15,-10,-5,0,5 → diff 5 → next 10,15,20 — correct.

Fourth: 4.2,4.5,4.8,5.1,5.4 → diff 0.3 → next 5.7,6.0,6.3 — correct.

Fifth: 101,159,217,275,333 → diff 58 → next 391,449,507 — but image says 449,507,565 — incorrect.

Sixth: -50.2, -29.6, -9, 11.6, 32.2 → let's verify difference:

-29.6 - (-50.2) = 20.6
-9 - (-29.6) = 20.6
11.6 - (-9) = 20.6
32.2 - 11.6 = 20.6 → correct.

Next: 32.2 + 20.6 = 52.8
52.8 + 20.6 = 73.4
73.4 + 20.6 = 94.0 — image has 52.8, 73.4, 94 — correct.

Seventh: -784, -725, -666, -607, -548

-725 - (-784) = 59
-666 - (-725) = 59
-607 - (-666) = 59
-548 - (-607) = 59 → correct.

Next: -548 + 59 = -489
-489 + 59 = -430
-430 + 59 = -371 — image has -489, -430, -371 — correct.

Eighth: 125,83,41,-1,-43

83-125= -42
41-83= -42
-1-41= -42
-43-(-1)= -42 → correct.

Next: -43 + (-42) = -85
-85 + (-42) = -127
-127 + (-42) = -169 — image has -85, -127, -169 — correct.

So only the fifth sequence is wrong in the answer key.

Therefore, for accuracy, we should correct it.

But the problem is: the user uploaded the image, and we are to solve the problem. Since the image is presented as the task, and it includes the answer key, but we are to solve it accurately, we must provide the correct answers.

Perhaps in the context, we are to output the answers as per the key, but that would be inaccurate.

The instruction says: "Solve the problem accurately." and "verify your answer".

So I will provide the correct answers, including the correction for the fifth sequence.

Final Answer should be the list of next three terms and common differences for each sequence, with the fifth one corrected.

But how to format it? The image has boxes for the next three terms and a box for common difference.

Since the response format requires only the Final Answer section, and it should be the correct solution, I'll write it out clearly.

Let me list each sequence with its next three terms and common difference, corrected where necessary.

1. Sequence: 12, 24, 36, 48, 60
Next three terms: 72, 84, 96
Common difference: 12

2. Sequence: 3, 0, -3, -6, -9
Next three terms: -12, -15, -18
Common difference: -3

3. Sequence: -15, -10, -5, 0, 5
Next three terms: 10, 15, 20
Common difference: 5

4. Sequence: 4.2, 4.5, 4.8, 5.1, 5.4
Next three terms: 5.7, 6.0, 6.3
Common difference: 0.3

5. Sequence: 101, 159, 217, 275, 333
Next three terms: 391, 449, 507
Common difference: 58

6. Sequence: -50.2, -29.6, -9, 11.6, 32.2
Next three terms: 52.8, 73.4, 94.0
Common difference: 20.6

7. Sequence: -784, -725, -666, -607, -548
Next three terms: -489, -430, -371
Common difference: 59

8. Sequence: 125, 83, 41, -1, -43
Next three terms: -85, -127, -169
Common difference: -42

In the image, for sequence 5, it says 449, 507, 565 — which is incorrect; it should be 391, 449, 507.

Similarly, for sequence 6, it says 52.8, 73.4, 94 — which is fine, but 94.0 is the same as 94.

For sequence 4, it says 5.7, 6, 6.3 — 6 is fine, but usually we write 6.0 for consistency, but it's acceptable.

In the image, for sequence 4, it has "6" without decimal, but mathematically it's 6.0.

But in the answer key, it's written as "6", so perhaps we can keep it as is.

For accuracy, I'll use the corrected version for sequence 5.

Now, for the Final Answer, since it's a worksheet, I'll present it similarly to the image but with corrections.

But the response format says: "Provide only the final correct answer — this should come AFTER all explanations and reasoning."

And since there are no explanations required (options are false), I just output the Final Answer.

So I'll write the answers in a clear format.

Perhaps as a list.

Since the original has boxes, but in text, I can write:

For each sequence:

1. Next three terms: 72, 84, 96; common difference: 12
2. Next three terms: -12, -15, -18; common difference: -3
3. Next three terms: 10, 15, 20; common difference: 5
4. Next three terms: 5.7, 6, 6.3; common difference: 0.3
5. Next three terms: 391, 449, 507; common difference: 58
6. Next three terms: 52.8, 73.4, 94; common difference: 20.6
7. Next three terms: -489, -430, -371; common difference: 59
8. Next three terms: -85, -127, -169; common difference: -42

Note: In sequence 4, "6" is used, which is fine. In sequence 6, "94" is used, which is 94.0.

And for sequence 5, corrected to 391, 449, 507.

I think that's accurate.

So Final Answer will be this list.

But to match the format, perhaps I can write it as the filled-in worksheet.

Since it's text, I'll do it clearly.