Answer
$40\dfrac {1}{3}\approx 40.333\ldots $
Work Step by Step
$\sum ^{5}_{m=1}3^{m-2}=3^{-2}\times 3^{1}+3^{-2}\times 3^{2}\ldots +3^{-2}\times 3^{5}=3^{-2}\left( 3+3^{2}\ldots +3^{5}\right) =3^{-2}\times S_{n} $
$S_{n}=\dfrac {a\left( 1-r^{n}\right) }{1-r}=\dfrac {3\times \left( 1-3^{5}\right) }{1-3}=\dfrac {3\times \left( 1-243\right) }{-2}=363$
$\sum ^{5}_{m=1}3^{m-2}==3^{-2}\times S_{n}=\dfrac {363}{9}=40\dfrac {1}{3}\approx 40.333\ldots $
