Question

Find the common ratio r of an infinite geometric series with first term 9 and sum of terms 15.

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Answer 1

Given:

First term = 9

Sum of the terms = 15

To find:

The value of the common ratio

Solution:

We have given the infinite geometric progression.

Where the value of the terms is not defined means the number of the terms cannot be counted.

so we take the value of the n as ∞

where the sum of the terms is given by:

$s = \frac{a}{1-r}$

here a is the first term

r is a common ratio and s is the sum of the terms

now put the given terms in the formula we get

$15 = \frac{9}{1-r}$

15(1-r) = 9

15 - 15r = 9

15r = 15-9

15r = 6

r = 6/15

r = 2/5

r = 0.4

Hence, The value of the common ratio is 0.4