Question

The number which should be added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P., is.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

Answer 2

Suppose that the added number be $x$

then $x + 2 , x + 14 , x + 62$ be in G.P.

Therefore $( x + 14 ) ^ { 2 } = ( x + 2 ) ( x + 62 )$

$\Rightarrow$ $x ^ { 2 } + 196 + 28 x = x ^ { 2 } + 64 x + 124$

$\Rightarrow$ $36 x = 72 \Rightarrow x = 2$.

Trick : (1) Let 1 is added, then the numbers will be 3, 15, 63 which are obviously not in G.P.

(2) Let 2 is added, then the numbers will be 4, 16, 64 which are obviously in G.P.