Question

How many terms of the series 3, 9, 27 . . . . . . . will add up to 363?

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Answer 1

The given sequence is a G.P. with a = 3 and r = 3. Sum of first n terms is 363.

Sum of n terms = $\frac{a(r^n-1)}{r-1}$

$=\frac{3\times 3^{10}-1}{3-1}$

$\Rightarrow$ $\frac{3r}{2}$ ($3^n$ - 1) = 363

$\Rightarrow$ $3^n$ = 1 + $\frac{363}{3}$ $\times$ 2

= 243

$3^n$ = 243 = $3^5$

$3^n$ = $3^5$

n = 5