Sequence And Series Question 580
Question: The number which should be added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P., is
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
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+28x=x^{2}+64x+124 $
$ \Rightarrow $ $ 36x=72\Rightarrow 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.
BETA
