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The number which should be added to the numbers $2,14,62$ so that the resulting numbers may be in G.P., is
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2325 Upvotes
Verified Answer
The correct answer is:
$2$
Suppose that the added number be $x$
then $x+2, x+14, x+62$ be in G.P.
Therefore $(x+14)^2=(x+2)(x+62)$
$\Rightarrow \quad x^2+196+28 x=x^2+64 x+124$
$\Rightarrow 36 x=72 \Rightarrow x=2$
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.
then $x+2, x+14, x+62$ be in G.P.
Therefore $(x+14)^2=(x+2)(x+62)$
$\Rightarrow \quad x^2+196+28 x=x^2+64 x+124$
$\Rightarrow 36 x=72 \Rightarrow x=2$
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.
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