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JAMB Mathematics 2016 Paper

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Question : 5

Total: 50

If the 2nd term of a G.P is

\frac{8}{9}

and the 6th term is 4

\frac{1}{2}

. Find the common ratio.

2
$\frac{3}{2}$
$\frac{2}{3}$
3

Solution:

Concept:

Use the formula for the

n

th term of a geometric progression:

T_n = ar^{n-1}

.

Explanation:

Given

T_2 = \frac{8}{9}

, so

ar = \frac{8}{9}

.

Given

T_6 = 4\frac{1}{2} = \frac{9}{2}

, so

ar^5 = \frac{9}{2}

.

Divide the second equation by the first:

\frac{ar^5}{ar} = \frac{\frac{9}{2}}{\frac{8}{9}}

r^4 = \frac{9}{2} \times \frac{9}{8} = \frac{81}{16}

Take the fourth root:

r = \sqrt[4]{\frac{81}{16}} = \frac{3}{2}

Answer:

The common ratio is

\frac{3}{2}

, which is option B.

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