Question

If the $k^{th}$ term of the arithmetic progression 25, 50,75, 100, $\dots \dots$ is 1000, then find the value of k.

Answer 1

Let $a$ be the first term and $d$ be their common difference of the AP.
Then, $nth$ term of the AP $T_n=a+(n-1)d$
Here, in the given AP,. $a=25;d=50-25=25$
Given, $T_k=1000$
$=>25+(k-1)25=1000$
$=>25+25k-25=1000$
$=>25k=1000$
$=>k=40$