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Sequence and Series

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Question : 8 of 86

Marks: +1, -0

Find the sum of 10 terms G.P with first term and common ratio being 8 and 3 respectively

$2,63,291$
$-2,36,192$
$2,19,631$
$2,36,192$

Solution:

Concept:

Sum of

n

terms of a geometric progression:

S_n = a \frac{r^n - 1}{r - 1}

for

r \neq 1

.

Explanation:

Given first term

a = 8

, common ratio

r = 3

, and number of terms

n = 10

.

Compute

r^{10} = 3^{10} = 59049

.

Use formula:

S_{10} = 8 \cdot \frac{3^{10} - 1}{3 - 1} = 8 \cdot \frac{59049 - 1}{2}

.

Simplify:

8 \cdot \frac{59048}{2} = 8 \cdot 29524 = 236192

.

Answer:

The sum is

236192

, which corresponds to option D.

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