Test Index

Sequence and Series

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Question : 75 of 86

Marks: +1, -0

Find the three numbers in G.P, whose sum is 19 and product is

216 .

$9,6,4$ or $4,6,9$
$9,6,3$ or $3,6,9$
$9,3,1$ or $1,3,9$
$9,3,-1$ or $-1,3,9$

Solution:

Concept:

Let the three numbers in GP be

\frac{a}{r}

,

a

,

ar

. Their product is

a^3

.

Explanation:

Product:

\frac{a}{r} \cdot a \cdot ar = a^3 = 216

→

a = 6

.

Sum:

\frac{6}{r} + 6 + 6r = 19

→

\frac{6}{r} + 6r = 13

.

Multiply by

r

:

6 + 6r^2 = 13r

→

6r^2 - 13r + 6 = 0

.

Factor:

(3r-2)(2r-3)=0

→

r = \frac{2}{3}

or

r = \frac{3}{2}

.

Thus numbers: For

r=\frac{2}{3}

:

\frac{6}{2/3}=9

,

6

,

6\cdot\frac{2}{3}=4

→

9,6,4

.

For

r=\frac{3}{2}

:

\frac{6}{3/2}=4

,

6

,

6\cdot\frac{3}{2}=9

→

4,6,9

.

Answer:

Option A:

9,6,4

or

4,6,9

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