The 3^rd term of an arithmetic sequence is 10 and its 8^th term is 25. What is its 4^th term? And the 13^th term?

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Solution

3^rd term of the arithmetic sequence = 10

8^th term of the arithmetic sequence = 25

To get the 8^th term from the 3^rd term, we must add the common difference 5 times to the 3^rd term.

The number to be added is 25 − 10 = 15

∴ Common difference = = 3

To get the 4^th term from the 3^rd term, we must add the common difference once to the 3^rd term.

∴ 4^th term = 10 + 1 × 3 = 10 + 3 = 13

To get the 13^th term from the 3^rd term, we must add the common difference ten times to the 3^rd term.

∴ 13^th term = 10 + 10(3) = 10 + 30 = 40

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