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JAMB Mathematics 2019 Paper

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Question : 60

Total: 73

If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.

$\frac{1}{3}$
$\frac{1}{9}$
$\frac{2}{3}$
$\frac{2}{9}$

Solution:

Concept:

Use the general term formula for a geometric progression:

T_n = ar^{n-1}

.

Explanation:

For the 3rd term:

T_3 = ar^2 = 9

.

For the 7th term:

T_7 = ar^6 = \frac{1}{9}

.

Divide the equation for

T_7

by the equation for

T_3

:

\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}

This simplifies to:

r^4 = \frac{1}{81}

Since

\frac{1}{81} = \left(\frac{1}{3}\right)^4

, we get:

r^4 = \left(\frac{1}{3}\right)^4

Taking the fourth root gives the common ratio:

r = \frac{1}{3}

Answer:

The common ratio is

\frac{1}{3}

.

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