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# How many terms of the series 2 + 6 + 18 + …. + must be taken to make the

Question:

How many terms of the series 2 + 6 + 18 + …. + must be taken to make the sum equal to 728?

Solution:

Sum of a G.P. series is represented by the formula $S_{n}=a \frac{r^{n}-1}{r-1}$ hen 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.

Here,

a = 2

r = (ratio between the n term and n-1 term) 6 ÷ 2 = 3

$S_{n}=728$

$\therefore 728=2 \times \frac{3^{n}-1}{3-1}$

$\Rightarrow 728=2 \times \frac{3^{\mathrm{n}}-1}{2}$

$\Rightarrow 728=3^{\mathrm{n}}-1$

$\Rightarrow 728+1=3^{\mathrm{n}}$

$\Rightarrow 729=3^{\mathrm{n}}$

$\Rightarrow 3^{6}=3^{\mathrm{n}}$

$\therefore \mathrm{n}=6$

$\therefore 6$ terms must be taken to reach the desired answer.