Find the sum of the GP :


Find the sum of the GP :

$0.15+0.015+0.0015+\ldots .$ To 6 terms



Sum of a G.P. series is represented by the formula, $\mathrm{S}_{\mathrm{n}}=\mathrm{a} \frac{1-\mathrm{r}^{\mathrm{n}}}{1-\mathrm{r}}$

when |r|<1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms


a = 0.15

r = (ratio between the n term and n-1 term) 0.015 ÷ 0.15 = 0.1

n = 6 terms

$\Rightarrow \mathrm{S}_{\mathrm{n}}=0.15 \times \frac{1-0.1^{6}}{1-0.1}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=0.15 \times \frac{1-0.000001}{0.9}$

$\Rightarrow \mathrm{S}_{\mathrm{n}}=0.15 \times \frac{0.999999}{0.9}$

$\therefore \mathrm{S}_{\mathrm{n}}=16.67$


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