Question

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

Answer 1

Given series is $11,8,5,\mathrm{2............}$

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

$T_n=-150$

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

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

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

$\Rightarrow 14-3n=-150$

$\Rightarrow -3n=-164$

$\therefore n=\frac{-164}{-3}=54.66$

$n$ cannot be a fraction.

So, it is not in A.P.