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 $d$ .

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

medium

The sum of the first

n

terms of

4, 7, 10, \ldots

is 175. Find

n

Example 2

medium

How many terms of

7, 12, 17, \ldots

are needed to reach

82

Example 3

medium

Find the sum

20 + 17 + 14 + \ldots + (-7)

Example 4

challenge

The sum of the first

10

terms of an arithmetic sequence is

145

, and the sum of the next

10

terms is

445

. Find

a_1

and

d

Example 5

medium

An arithmetic sequence has

a_1=2

and

a_{10}=29

. Find

d

and the sum of the first 10 terms.

Example 6

hard

The sum of the first

n

terms of an arithmetic sequence is

S_n = 2n^2 + 3n

. Find

a_1

and

d

Example 7

easy

5, 10, 20, 40, \ldots

arithmetic or geometric?

Example 8

medium

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

Example 9

easy

Find the sum of the first 5 terms of

2, 4, 6, 8, 10

Example 10

medium

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

a_1

and

d

Example 11

medium

In an arithmetic sequence,

a_5=20

and the common difference is 3. Find the sum of the first 5 terms.

Example 12

medium

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

Example 13

medium

Find the sum

S = 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

a_1

and

d

Example 15

easy

How many terms are there from

a_5

a_{20}

inclusive?

Example 16

easy

Find the 8th term of an arithmetic sequence with

a_1 = 2

and

d = 5

Example 17

medium

Find the sum of the first

50

positive odd numbers.

Example 18

medium

Find the 12th term of an arithmetic sequence whose first three terms are

-2, 1, 4

Example 19

medium

In an arithmetic sequence

a_5 = 18

and

a_{12} = 46

. Find

a_1

and

d

Example 20

medium

An arithmetic sequence has

a_3 = 11

and

a_8 = 31

. Find

a_{15}

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Related Concepts

Sequence Geometric Sequence