Question

The sum of $n$ terms of the series $2,5,8,....$ is $950$ : find $n$.

Answer 1

Given series is $2,5,8,........$

Given that the sum of $n$ terms of the series is $950$

The first term of the series is $a=2$ and the common difference is $d=5-2=3$

We know that the sum of $n$ terms of an AP is $\frac{n}{2}(2a+(n-1\left)d\right)$

$\Rightarrow \frac{n}{2}(2a+(n-1\left)d\right)=950$

$\Rightarrow \frac{n}{2}(4+(n-1)\times 3)=950$

$\Rightarrow n(3n+1)=1900$

$\Rightarrow 3n^2+n-1900=0$

$\Rightarrow n=\frac{-1\pm \sqrt{22801}}{6}=\frac{-1\pm 151}{6}=25,-\frac{152}{6}$

Since $n$ is an positive integer , we get $n=25$