Find the sum of 25 terms of the AP

Question:
Find the sum of 25 terms of the AP $\sqrt{2}, 2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, \ldots$

Solution:

To Find: The sum of 25 terms of the given AP series

Sum of $n$ terms of an $A P$ with first term a and common difference $d$ is given by

$S=\frac{n}{2}[2 a+(n-1) d]$

Here,

$a=\sqrt{2}, n=25, d=\sqrt{2} \Rightarrow S=\frac{25}{2}[2 \sqrt{2}+24 \sqrt{2}]$

$=25 \times 13 \times \sqrt{2}=325 \sqrt{2}$

Sum of 25 terms is $325 \sqrt{2}$.