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

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

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

= 243

$3^n=243=3^5$

$3^n=3^5$

n = 5