Practice Arithmetic Sequence in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A sequence where each term is obtained from the previous by adding a fixed constant called the common difference dd.

Add the same number each time — 2, 5, 8, 11,... (add 3 each step). This is constant-rate growth.

Showing a random 20 of 50 problems.

Example 1

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The sum of the first nn terms of 4,7,10,…4, 7, 10, \ldots is 175. Find nn.

Example 2

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How many terms of 7,12,17,…7, 12, 17, \ldots are needed to reach 8282?

Example 3

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Find the sum 20+17+14+…+(−7)20 + 17 + 14 + \ldots + (-7).

Example 4

challenge
The sum of the first 1010 terms of an arithmetic sequence is 145145, and the sum of the next 1010 terms is 445445. Find a1a_1 and dd.

Example 5

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An arithmetic sequence has a1=2a_1=2 and a10=29a_{10}=29. Find dd and the sum of the first 10 terms.

Example 6

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The sum of the first nn terms of an arithmetic sequence is Sn=2n2+3nS_n = 2n^2 + 3n. Find a1a_1 and dd.

Example 7

easy
Is 5,10,20,40,…5, 10, 20, 40, \ldots arithmetic or geometric?

Example 8

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Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...

Example 9

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Find the sum of the first 5 terms of 2,4,6,8,102, 4, 6, 8, 10.

Example 10

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The 3rd term of an arithmetic sequence is 14 and the 7th term is 30. Find a1a_1 and dd.

Example 11

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In an arithmetic sequence, a5=20a_5=20 and the common difference is 3. Find the sum of the first 5 terms.

Example 12

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The 2nd term is 11 and the 5th term is 23. Find the 8th term.

Example 13

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Find the sum S=2+5+8+…+59S = 2 + 5 + 8 + \ldots + 59.

Example 14

challenge
The 4th term of an arithmetic sequence equals 3 times the 1st term, and the 6th term is 13. Find a1a_1 and dd.

Example 15

easy
How many terms are there from a5a_5 to a20a_{20} inclusive?

Example 16

easy
Find the 8th term of an arithmetic sequence with a1=2a_1 = 2 and d=5d = 5.

Example 17

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Find the sum of the first 5050 positive odd numbers.

Example 18

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Find the 12th term of an arithmetic sequence whose first three terms are −2,1,4-2, 1, 4.

Example 19

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In an arithmetic sequence a5=18a_5 = 18 and a12=46a_{12} = 46. Find a1a_1 and dd.

Example 20

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An arithmetic sequence has a3=11a_3 = 11 and a8=31a_8 = 31. Find a15a_{15}.
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