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

Given:

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

To do:

We have to find the 50th term of the A.P.

Solution:

Let the common difference of the A.P. be $d$.

First term $a_1=a=5$

We know that,

nth term of an A.P. $a_n=a+(n-1)d$

Therefore,

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

$-292=5+99d$

$99d=-292-5$

$99d=-297$

$d=\frac{-297}{99}$

$d=-3$......(i)

This implies,

$a_{50}=a+(50-1)d$

$=5+49d$

$=5+49(-3)$

$=5-147$

$=-142$

Hence, the 50th term of the given A.P. is $-142$.