Question

Find the sum of first 25 terms of an AP whose nth term is given by an=3n+2

Answer 1

hope it helps you ok

Answer 2

$\sf{Answer -}$

The sum of first 25 terms of AP is 1025.

$\sf{Step-by-step\:explanation -}$

Given,

$a_{n}=3n+2$

So,

$a_{1}=3(1)+2=5$

$a_{2}=3(2)+2=8$

$a_{3}=3(3)+2=11$

So, the AP with nth term as $3n+2$ is 5,8,11.............

Here, we get -

$a=5$

$d=3$

Using the formula -

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

$\implies S_{25}=\frac{25}{2}[2\times 5+(25-1)3]$

$\implies S_{25}=\frac{25}{2}(10+72)$

$\implies S_{25}=1025$

Thus the sum is 1025.