Question
The number which should be added to the number added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P. is
Answer: Option B
:
B
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)
⇒x2+196+28x = x2+64x+124
⇒36x = 72 ⇒x = 2
Trick : (a) Let 1 is added, then the numbers will be 3, 15, 63 which are obviously not in G.P.
(b) Let 2 is added, then the numbers will be 4, 16, 64 which are obviously in G.P.
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:
B
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)
⇒x2+196+28x = x2+64x+124
⇒36x = 72 ⇒x = 2
Trick : (a) Let 1 is added, then the numbers will be 3, 15, 63 which are obviously not in G.P.
(b) Let 2 is added, then the numbers will be 4, 16, 64 which are obviously in G.P.
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