Question

If for a sequence,$t_n=\frac{2^{n-2}}{5^{n-3}}$,show that the sequence is a G.P . Find its first term and common ratio.

Answer 1

Given: $t_n=\frac{2^{n-2}}{5^{n-3}}$

First term $=t_1=\frac{2^{1-2}}{5^{1-3}}=\frac{2^{-1}}{5^{-2}}=\frac{25}{2}$

Second term$t_2=\frac{2^{2-2}}{5^{2-3}}=\frac{2^0}{5^{-1}}=5$

Common ratio $=5÷\frac{25}{2}=5\times \frac{2}{25}=\frac{2}{5}$