Question

Check whether $-105$ is a term of the A.P. $12,10,8,6$ .........

• A. $-105$ is not a term of this A.P.
• B. $105$ is a term of this A.P.
• C. $-105$ is an integer
• D. $105$ is not an integer

Answer 1

The correct option is A $-105$ is not a term of this A.P.

Given series is $12,10,8,6,....$

Thus $a=12,d=-2,a_n=-105$
Let $-105$ be the $n^{th}$ term of this A.P.
Since, $a_n=a+(n-1)d$
$\Rightarrow 105=12+(n-1)(-2)$
$\Rightarrow -105-12=-2n+2$
$\Rightarrow -117-2=-2n$
$\Rightarrow n=\frac{-119}{-2}$
Clearly, $n$ is an integer after solving this.
Therefore, $-105$ is not a term of this A.P.