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8. Sequences and Series
easy
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
$4$
Solution
(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 $G.P.$
Standard 11
Mathematics
