Given that [tex]a_1=24[/tex] and [tex]a_2=17[/tex], if [tex]a_n[/tex] is an arithmetic sequence, then the common difference between successive terms is [tex]d=a_2-a_1=17-24=-7[/tex].
You then have
[tex]a_2=a_1+d[/tex]
[tex]\implies a_3=a_2+d=a_1+2d[/tex]
[tex]\implies a_4=a_3+d=a_1+3d[/tex]
[tex]\implies \cdots\implies a_n=a_{n-1}+d=\cdots=a_1+(n-1)d[/tex]
So the explicit formula for the [tex]n[/tex]th term is
[tex]a_n=24-7(n-1)[/tex]
