Single Choice

Sum of 20 terms of $$3 + 6 + 12 + ...$$ is

A$$3(2^{^{20}}-1)/2$$
B$$3(2^{^{19}}-1)/2$$
C$$3(2^{^{20}}-1)$$
Correct Answer
D$$3(2^{^{19}}-1)$$

Solution

Sum of the series in G.P upto n terms is

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

$$a=3, r=2, n=20$$

$$\therefore$$The sum to n terms is $$S= 3\; (2^{20}\; -\; 1) $$

SIMILAR QUESTIONS

Sequences and Series

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

Sequences and Series

How many terms of the series $$1+3+9+ ...$$sum to $$121$$?

Sequences and Series

Evaluate $$\displaystyle \sum _{ k=1 }^{ 11 }{ { (2+3 }^{ k }) } $$

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How many terms of G.P $$\displaystyle 3, { 3 }^{ 2 }, { 3 }^{ 3 }, ...$$ are needed to give the sum $$120$$?

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The sum of first three terms of a G.P. is $$16$$ and the sum of next three terms is $$128$$. Determine the first term, the common ratio and the sum to $$n$$ terms of the G.P.

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The sum of some terms of G.P. is $$315$$ whose first term and the common ratio are $$5$$ and $$2$$, respectively. Find the last term and the number of terms .

Sequences and Series

Let there be $$a_1, a_2, a_3, \dots, a_n$$ terms in G.P. whose common ratio is r. Let $$S_k$$ denote the sum of first k terms of this G.P. Prove that $$S_{m-1} S_m = \frac{r+1}{r} \displaystyle \sum_{i < j}^{m} a_ia_j$$.

Sequences and Series

Let $$a_1, a_2, ..... , a_n$$ be real numbers such that $$\sqrt{a_1} + \sqrt{a_2 - 1} + \sqrt{a_3 - 2} + \dots + \sqrt{a_n - (n-1)} = \frac{1}{2} ( a_1, a_2, ..... , a_n) = \dfrac{n (n-3)}{4}$$. Compute the value of $$\displaystyle \sum_{i=1}^{100} a_i$$.

Sequences and Series

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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