Question

State whether the given statement is true or false:

$-150$ is a term of A.P. $17,12,7,2,.........$

• A. True
• B. False

Answer 1

The correct option is B False

$17,12,7,\mathrm{2.............}$

$a=17,d=12-17=-5$

Let $a_n=-150$

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

$17+\left(n-1\right)\left(-5\right)=-150$

$17-5n+5=-150$

$22-5n=-150$

$5n=22+150$

$5n=172$

$\Rightarrow n=\frac{172}{5}$

$\Rightarrow n=34.4$ which is not a natural numbers

Hence, $-150$ is not a term of given A.P