Question

The $7^{th}$ term of an A.P. is $20$ and its ${13}^{th}$ term is $32$. Find the first term of A.P.

Answer 1

Solution:-

Given:-

$a_7=20$

$a_{13}=32$

$a=?$

As we know that,

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

$\therefore a_7=20$

$\Rightarrow a+6d=20⟶\left(1\right)$

$a_{13}=32$

$\Rightarrow a+12d=32⟶\left(2\right)$

Multiplying ${eq}^n\left(1\right)$ by 2, we have

$\Rightarrow 2a+12d=40⟶\left(3\right)$

Subtracting ${eq}^n\left(2\right)$ from $\left(3\right)$, we have

$2a+12d-(a+12d)=40-32$

$2a+12d-a-12d=8$

$a=8$

$\therefore$ First term of given A.P. is 8.

Hence the correct answer is 8.