Question

^{_{\(\left(\dfrac{2}{5}\right)^{X+1}-\left(\dfrac{2}{5}\right)^X=\left(\dfrac{-12}{125}\right)\)}}

Answer 1

\(\Leftrightarrow\left(\dfrac{2}{5}\right)^n\left(\dfrac{2}{5}-1\right)=\dfrac{-12}{125}\)

\(\Leftrightarrow\left(\dfrac{2}{5}\right)^n\left(\dfrac{-3}{5}\right)=\dfrac{-12}{125}\)

\(\Leftrightarrow\left(\dfrac{2}{5}\right)^n=\dfrac{4}{25}=\left(\dfrac{2}{5}\right)^2\)

\(\Rightarrow n=2\)