Question

Is $-150$ a term of the $AP11,8,5,2?$

Answer 1

Given $AP$ is $11,8,5,2,\cdots$

Common difference is $d=8-11=-3$

First term is $a=11$

Let the $n^{th}$ term be $-150$

$⟹11+(n-1)(-3)=-150$

$⟹-3(n-1)=-161$

$⟹n=\frac{161}{3}+1=\frac{164}{3}$

As $n$ is not an integer So $-150$ is not a term of $AP$