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