Question

Is $-150$ a term of $11,8,5,2,...........?$

Answer 1

Given : first term $\left(a\right)=11$, common difference $\left(d\right)=8-11=-3$​

Let $-150$ be the nth term, and $n^{th}$ term is given by $a_n=a+(n-1)d$

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

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

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

$\Rightarrow -150=14-3n$

$\Rightarrow 3n=150+14$

$\Rightarrow 3n=164$

$\Rightarrow n=\frac{164}{3}$

number of terms, i.e ${}^{\prime }{n}^{\prime }$ cannot be in fraction.

So, $-150$ is not a term of the given AP.