Question

An arithmetic sequence is given below.

Answer 1

Given that $a_1=24$ and $a_2=17$, if $a_n$ is an arithmetic sequence, then the common difference between successive terms is $d=a_2-a_1=17-24=-7$.

You then have

$a_2=a_1+d$
$\implies a_3=a_2+d=a_1+2d$
$\implies a_4=a_3+d=a_1+3d$
$\implies \cdots\implies a_n=a_{n-1}+d=\cdots=a_1+(n-1)d$

So the explicit formula for the $n$th term is

$a_n=24-7(n-1)$