Question

Find $n$ if the given value of $x$ is the $n$th term of the given A.P.
$25,50,75,100,......;x=1000$

Answer 1

Given sequence is $25,50,75,100,...$

The first term $a=25$ and

the common difference $d=50-25=25$

Given that the $n^{th}$ term is $1000$

We know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=1000$

$⟹25+(n-1)\ast \left(25\right)=1000$

$⟹25-25+25n=1000$

$⟹25n=1000$

$⟹n=\frac{1000}{25}$

$⟹n=40$