Question

For the AP: $x-7,x-2,x+3,....$ the ${15}^{th}$ term is ____.

• A. $x+53$
• B. $x-53$
• C. $x-63$
• D. $x+63$

Answer 1

The correct option is D

$x+63$

Given AP is: $x-7,x-2,x+3,....$
$\therefore$ First term $\left(a\right)=x-7$

Common difference: $\left(d\right)=(x-2)-(x-7)=5$

The $n^{th}$ term of an AP is given by, $a_n=a+(n-1)d$

Then, the ${15}^{th}$ term of the above series is given by,

$a_{15}=(x-7)+(15-1)5$

$\Rightarrow a_{15}=x-7+70=x+63$