First slide

Geometric progression

Question

There are four numbers of which the first three are in G.P. whose common ratio is $\frac{1}{2}$ and the last three are in A.P. If the last number is two less than the first, then the four members are

Moderate

A

$3, 1, \frac{1}{3}, - \frac{1}{3}$
B

$2, 1, \frac{1}{2}, 0$
C

$4, 1, \frac{1}{4}, - \frac{1}{2}$
D

None of these

Solution

The numbers can be taken as $a, \frac{a}{2}, \frac{a}{4}, a - 2$ .
By question, $\frac{a}{2}, \frac{a}{4}, a - 2$ are in AP.
$∴ 2 \cdot \frac{a}{4} = \frac{a}{2} + a - 2; or a = 2 .$
Hence, the numbers are $2, 1, \frac{1}{2}, 0$ .

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