Question

If sum of $3rd$ and $8th$ terms of an $A.P.$ is $7$ and sum of $7th$ and $14th$ terms is $-3$ then find the $10th$ term.

Answer 1

nth term $t_n=a+(n-1)d$

$a=$ First term

$d=$ Common difference

$n=$ number of terms

$t_n=n^{th}$ term

$a_3+a_8=7a+2d+a+7d=72a+9d=7⟶\left(i\right)$ $a_7+a_{14}=-3a+6d+a+13d=-32a+19d=-3⟶\left(ii\right)$

From $\left(i\right)$ & $\left(ii\right)$

$2a+9d=72a+19d=-3$

$-10d=10d=-1,a=8.$

$a_{10}=a+9d=8+9(-1)=-1$