Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.3 Geometric Sequences and Series - 14.3 Exercise Set - Page 912: 34

$a_n=5\times(\frac{m}{2})^{n-1}$

The general term in a geometric sequence is: $a_n=a_1\times r^{n-1}$ Here, $a_1=5$ We can find the common ratio by dividing two subsequent terms: $r=\frac{a_2}{a_1}=\frac{\frac{5m}{2}}{5}=\frac{m}{2}$ The general term is: $a_n=5\times\frac{m}{2}^{n-1}$