Arithmetic Sequences Notes and Worksheets - Lindsay Bowden - Free Printable

Let’s go step by step through each problem.

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1. Is the sequence finite or infinite? {9, 12, 15, 18}

This sequence has only 4 numbers listed and no “...” at the end. That means it stops — it doesn’t keep going forever.

✔ So, this is a finite sequence.

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2. Find the next three terms in the sequence. {8, 2, -4, -10...}

Look at how we get from one number to the next:

- 8 → 2: subtract 6
- 2 → -4: subtract 6
- -4 → -10: subtract 6

So the pattern is: subtract 6 each time.

Next term after -10:
-10 - 6 = -16

Then:
-16 - 6 = -22

Then:
-22 - 6 = -28

✔ Next three terms: -16, -22, -28

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3. What is the common difference in this sequence? {54, 63, 72, 81...}

Common difference means: what do you add (or subtract) to get from one term to the next?

Check:

- 63 - 54 = 9
- 72 - 63 = 9
- 81 - 72 = 9

✔ Common difference = 9

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4. Is this sequence an arithmetic sequence? {108, 90, 72, 54, 36...}

Arithmetic sequence = same amount added or subtracted each time.

Check differences:

- 90 - 108 = -18
- 72 - 90 = -18
- 54 - 72 = -18
- 36 - 54 = -18

Same difference every time → YES!

✔ This is an arithmetic sequence.

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5. What are the next 3 terms in the sequence? {3.5, 4.9, 6.3, 7.7...}

Find the pattern:

- 4.9 - 3.5 = 1.4
- 6.3 - 4.9 = 1.4
- 7.7 - 6.3 = 1.4

Add 1.4 each time.

Next term:
7.7 + 1.4 = 9.1

Then:
9.1 + 1.4 = 10.5

Then:
10.5 + 1.4 = 11.9

✔ Next three terms: 9.1, 10.5, 11.9

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6. What is the common difference in this arithmetic sequence? {1/3, 2/3, 1, 4/3}

First, write all as fractions with denominator 3:

- 1/3
- 2/3
- 1 = 3/3
- 4/3

Now check differences:

- 2/3 - 1/3 = 1/3
- 3/3 - 2/3 = 1/3
- 4/3 - 3/3 = 1/3

✔ Common difference = 1/3

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Final Answer:

1. Finite
2. -16, -22, -28
3. 9
4. Yes
5. 9.1, 10.5, 11.9
6. 1/3