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Paper 2 · June 2009 · Sequences and Series

The recurring decimal $5,4\dot{2}\dot{7}$ can be written as $5,4+0,027+0,00027+0,0000027+\ldots$ . What is the common ratio of the geometric series that follows the 5,4?

A0,001

B0,01

C0,027

D0,1

Explanation

Each term after

0{,}027

is the previous one divided by 100, since

0{,}00027=0{,}027\times0{,}01

. So the common ratio is

0{,}01

.

Derived from ZIMSEC Mathematics Paper 2, June 2009, Q1

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