Single Choice

How many terms of the series 1+3+9+ ...sum to 364?

A5
B6
Correct Answer
C4
D3

Solution

The above sequence is a G.P with a common difference of 3, and first term 1.
Thus sum of G.P is
$$S_{n}=\dfrac{1(3^{n}-1)}{3-1}$$

$$=\dfrac{3^{n}-1}{2}$$

$$S_{n}=364$$
Hence

$$\dfrac{3^{n}-1}{2}=364$$

$$3^{n}-1=728$$

$$3^{n}=729$$

$$3^{n}=3^{6}$$

$$n=6$$.

SIMILAR QUESTIONS

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Find four terms which are in G.P., whose third term is $$4$$ more than first term and second term is $$36$$ more than $$4^{th}$$ term.

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