check -25 is a term of AP $5, 3, 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . n$ .

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Solution

First term, a = 5 ; common difference, d = 3 - 5 = -2
As $a_{n} = a + (n - 1) d$ $\Rightarrow - 25 = 5 + (n - 1) (- 2)$
$- 30 = - 2 n + 2 \Rightarrow 2 n = 32 \Rightarrow n = 16$
$\Rightarrow - 25$ is $16^{t h}$ term of A.P.

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