The number which should be added to the numbe | vedclass

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Question

(b) Suppose that the added number be $x$

then $x + 2,\;x + 14,\;x + 62$ be in $G.P.$

Therefore ${(x + 14)^2} = (x + 2)(x + 62)$

$ \Rightarrow

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(b) Suppose that the added number be $x$

then $x + 2,\;x + 14,\;x + 62$ be in $G.P.$

Therefore ${(x + 14)^2} = (x + 2)(x + 62)$

$ \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 $G.P.$

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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