Question

The sum of the first five terms of the series will be.

• A. $39 \frac { 9 } { 16 }$
• B. $18 \frac { 3 } { 16 }$
• C. $39 \frac { 7 } { 16 }$
• D. $13 \frac { 9 } { 16 }$

Answer 1

Answer: (A)

$39 \frac { 9 } { 16 }$

Answer 2

Given series is

(in G.P.)

Here $a = 3 , r = \frac { 3 } { 2 }$ ,

then sum of the five terms

$S _ { 5 } = \frac { a \left( r ^ { n } - 1 \right) } { r - 1 } = \frac { 3 \left[ \left( \frac { 3 } { 2 } \right) ^ { 5 } - 1 \right] } { \frac { 3 } { 2 } - 1 } = \frac { 1 \left[ \frac { 3 ^ { 5 } } { 32 } - 1 \right] } { \frac { 1 } { 2 } }$

$= 6 \left[ \frac { 243 - 32 } { 32 } \right] = \frac { 211 \times 3 } { 16 } = \frac { 633 } { 16 } = 39 \frac { 9 } { 16 }$.