The sum to infinity of a geometric progression is -1/10 and the first term is -1/8. Find the common ratio of the progression.

Correct Answer is : −14-1/4−41

Correct Answer is : −14-1/4−41

Test Index

JAMB Mathematics 2012 Paper

Question : 18

Total: 48

-\frac{1}{10}

-\frac{1}{8}

. Find the common ratio of the progression.

Solution:

Concept:

The sum to infinity of a geometric progression is given by

S_{\infty} = \frac{a}{1-r}

, where

a

is the first term and

r

is the common ratio.

Explanation:

Substitute

S_{\infty} = -\frac{1}{10}

and

a = -\frac{1}{8}

into the formula.

-\frac{1}{10} = \frac{-\frac{1}{8}}{1-r}

This can be rewritten as:

-\frac{1}{10} = -\frac{1}{8(1-r)}

Multiply both sides by

-1

\frac{1}{10} = \frac{1}{8(1-r)}

Cross multiply.

8(1-r) = 10

Divide both sides by

8

1-r = \frac{10}{8} = \frac{5}{4}

Solve for

r

r = 1 - \frac{5}{4} = -\frac{1}{4}

Answer:

The common ratio of the progression is

-\frac{1}{4}

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