sum of the terms of an AP

Algebra Level 2

The fourth term of an arithmetic progression is 450. If the ninth term is 700, find the sum of the first thirty terms of this progression.

1 solution

A Former Brilliant Member
Dec 5, 2017

Given: $a_4=450$ and $a_9=700$

Working formula: $a_n=a_m+(n-m)(d)$

Solution:

$700=450+(9-4)(d)$ $\implies$ $d=50$

$a_{30}=a_4+(30-4)(50)=1750$

$a_1=a_4+(1-4)(d)=300$

The sum of the first thirty terms is

$s_{30}=\dfrac{n}{2}(a_1+a_{30})=15(300+1750)=\boxed{30750}$