find the second term of the arithmetic progression

Algebra Level pending

The $4^{th}$ and $17^{th}$ terms of an arithmetic progression are $40.5$ and $21$ , respectively. Find the $2^{nd}$ term of this progression.

1 solution

A Former Brilliant Member
Dec 17, 2017

The $n^{th}$ term of an arithmetic progression is given by $a_n=a_m+(n-m)(d)$ where $a_m$ is the $m^{th}$ term and $d$ is the common difference.

Computing for $d$ , we have

$21=40.5+(17-4)(d)$ $\implies$ $d=-1.5$

Computing for $a_2$ , we have

$a_2=40.5+(2-4)(-1.5)=43.5$