An A. P. consists of 60 terms. If the first and last terms be 7 and 125 respectively, find the $31^{s t}$ term.

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Solution

Given,n = 60, a1 = 7,

and a60 = 125

⇒ a1 + 59d = 125

7 + 59d = 125

59d = 118

d = 118/59 = 2

a31 = a1 + 30d = 7 + 30(2) = 7 + 60

∴ a31 = 67.

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