Question

If the sum of the $3^{rd}$ and the $8^{th}$ terms of an AP is 7 and the sum of the $7^{th}$ and the ${14}^{th}$ term is -3, find the ${10}^{th}$ term.

Answer 1

$a_3+a_8=7$

$a+2d+a+7d=7$

$2a+9d=7$ ...(1)

Also,

$a_7+a_{14}=-3$

$a+6d+a+13d=-3$

$2a+19d=-3$ ....(2)

$\left(2\right)-\left(1\right)$

$\Rightarrow 10d=-10$

$\Rightarrow d=-1$ and $2a=9+7\Rightarrow a=8$

Therefore, $a_{10}=a+9d=8-9=-1$