Question

The sum of $4^{\text{th}}$ and $8^{\text{th}}$ term of an A.P. is 24 and the sum of $6^{\text{th}}$ and ${10}^{\text{th}}$ term is 34. Find the first term and the common difference of A.P.

Answer 1

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

$T_4+T_8=24$

$a+3d+a+7d=24$

$a+5d=12$...(1)

$T_6+T_{10}=34$

$a+5d+a+9d=34$

$a+7d=17$...(2)

(2)-(1) gives:

$\therefore d=\frac{5}{2}$

From (1)

$a=17-7d$

$a=17-7\left(\frac{5}{2}\right)$

$\therefore a=-\frac{1}{2}$