Question

Is $-156$ a term of the AP $17,14,11,8...?$

Answer 1

The given AP is

$17,14,11,8....$

Here, first term, $a_1=17$

Common difference, $d=a_2-a_1=14-17=-3$

Let $-156$ is the $n$th term of this AP.

$a_n=-156$

$a+(n-1)d=-156$

$17+(n-1)(-3)=-156$

$-3(n-1)=-173$

$n-1=\frac{173}{3}$

$n=\frac{176}{3}$

$n$ is a fraction here. For, $-156$ to be a term of the AP, $n$ should be positive integer.

So, $-156$ is not a term of the AP