Check whether $- 150$ is a term of the AP : $11, 8, 5, 2.....$

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Solution

Given series is $11, 8, 5, 2............$

$a = 11$ and $d = 8 - 11 = - 3$

$T_{n} = - 150$

$a + (n - 1) d = - 150$

$\Rightarrow 11 + (n - 1) (- 3) = - 150$

$\Rightarrow 11 - 3 n + 3 = - 150$

$\Rightarrow 14 - 3 n = - 150$

$\Rightarrow - 3 n = - 164$

$∴ n = \frac{- 164}{- 3} = 54.66$

$n$ cannot be a fraction.

So, it is not in A.P.

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