Find the sum of the first 25 terms of an A.P. whose nth term is given by $a_n = 7 – 3n$.

Given:

nth term of an A.P. is given by $a_n = 7 – 3n$.

To do:

We have to find the sum of the first 25 terms.

Solution:

Here,

\( a_{n}=7-3n \)

Number of terms \( =25 \)

\( a_{1}=a=7-3 \times 1=7-3=4 \) 

\( a_{2}=7-3 \times 2=7-6=1 \)

\( \therefore d=a_{2}-a_{1}=1-4=-3 \)

We know that,

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

\( S_{25}=\frac{25}{2}[2 a+(25-1) d] \)

\( =\frac{25}{2}[2 \times 4+(25-1) \times (-3)] \)

\( =\frac{25}{2}[8+24 \times (-3)]=\frac{25}{2}[8-72] \)

\( =\frac{25}{2} \times (-64)=25 \times (-32)=-800 \)

The sum of the first 25 terms is $-800$.  

Tutorialspoint

Updated on: 10-Oct-2022

2K+ Views

Kickstart Your Career

Get certified by completing the course

Get Started