Test Index

Sequence and Series

© examsnet.com

Question : 63 of 86

Marks: +1, -0

If the fifth term of a G.P. is

3^{4}

and the second term is

3(2)^{3}

then the first term is

$2^{3}$
$3^{2}$
$4^{3}$
$2^{4}$

Solution:

Concept:

In a G.P., the

n

th term is

a r^{n-1}

where

a

is the first term and

r

is the common ratio.

Explanation:

Given: second term =

a r = 3 \cdot 2^3 = 24

and fifth term =

a r^4 = 3^4 = 81

.

Divide the fifth term by the second term:

\frac{a r^4}{a r} = r^3 = \frac{81}{24} = \frac{27}{8} = \left(\frac{3}{2}\right)^3

.

Thus

r = \frac{3}{2}

.

Then

a = \frac{\text{second term}}{r} = \frac{24}{3/2} = 24 \cdot \frac{2}{3} = 16 = 2^4

.

Answer:

2^4

© examsnet.com

Go to Question:

Prev Question

Next Question