Question

The first term of an A.P. is $5$ and its $100$th term is $-292$. Find the $50$th term of this A.P.

Answer 1

Given first term of A.P is $a_1=5$

100th term of A.P is $a_{100}=-292$

we know that the nth term of an A.P is given by

$a_n=a_1+(n-1)d$

hence $100$th term can be written as

$a_{100}=a_1+(100-1)d$

put value of $a_{100}=-292$ and $a_1=5$ we get

$-292=5+99d$

$99d=-292-5$

$⟹d=\frac{-297}{99}$

$⟹d=-3$

now for finding 50th term put $n=50,d=-3$ and $a_1=5$ in eq(1) we get

$a_{50}=5+(50-1)(-3)$

$⟹a_{50}=5-49\times 3$

$⟹a_{50}=5-147$

$⟹a_{50}=-142$