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8. Sequences and Series
medium
If the product of three consecutive terms of $G.P.$ is $216$ and the sum of product of pair-wise is $156$, then the numbers will be
A
$1, 3, 9$
B
$2, 6, 18$
C
$3, 9, 27$
D
$2, 4, 8$
Solution
(b) Let numbers are $\frac{a}{r},\;a,\;ar$
Under conditions, we get $\frac{a}{r}\;.\;a\;.\;ar = 216$
$ \Rightarrow $ $a = 6$
And sum of product pair wise $ = 156$
$ \Rightarrow $ $\frac{a}{r}\;.\;a + \frac{a}{r}\;.\;ar + a\;.\;ar = 156$
$ \Rightarrow $ $r = 3$
Hence numbers are $2, 6, 18.$
Trick : Since $2 \times 6 \times 18 = 216$ (as given) and no other option gives the value.
Standard 11
Mathematics
