Find the sum of $1 + 5 + 5^{2} + . . . .$ upto 8 terms.

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Solution

$\begin{matrix} s u m o f 1 + 5 + 5^{2} + 5^{3} . . . u p 8 t h t e r m s (a) F i r s t t e r m = 1 c o m m o n r a t i o (r) = 5 S u m o f 8 t h t e r m = \frac{a (r^{n} - 1)}{r - 1} = \frac{1 (5^{8} - 1)}{5 - 1} = \frac{5^{8} - 1}{4} \end{matrix}$

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