Test Index

Sequence and Series

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Question : 62 of 86

Marks: +1, -0

The number of terms in

6,18,54, . . . .1458

is

5
7
8
6

Solution:

Concept:

A geometric progression has the

n

th term

T_n = a r^{n-1}

, where

a

is the first term and

r

is the common ratio.

Explanation:

The given sequence is

6, 18, 54, \ldots, 1458

.

First term

a = 6

, common ratio

r = \frac{18}{6} = 3

.

Let the last term be the

n

th term:

6 \cdot 3^{n-1} = 1458

.

Divide both sides by

6

:

3^{n-1} = \frac{1458}{6} = 243

.

Since

243 = 3^5

, we have

n-1 = 5

, so

n = 6

.

Thus, there are 6 terms in the sequence.

Answer:

The number of terms is 6.

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