Question

Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is.

• A. 18
• B. 16
• C. 14
• D. None of these

Answer 1

Answer: (A)

18

Answer 2

Let three number of G.P. i.e., $a , a r , a r ^ { 2 }$

$a + a r + a r ^ { 2 } = 38$ and $a ^ { 3 } r ^ { 3 } = 1728$ …..(i)

$a \left( 1 + r + r ^ { 2 } \right) = 38$ …..(ii)

From equation (i) $a r = 12$ ⇒ $a = \frac { 12 } { r }$

From equation (ii) $\frac { 12 } { r } \left( 1 + r + r ^ { 2 } \right) = 38$

on solving $r = 2 / 3$ and $a = \frac { 12 \times 3 } { 2 } = 18$

Required number 18, 12, 8

Maximum number i.e., 18.