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8. Sequences and Series
easy
Three numbers are in $G.P.$ such that their sum is $38$ and their product is $1728$. The greatest number among them is
A
$18$
B
$16$
C
$14$
D
None of these
Solution
(a) Let three number of $G.P. $ $i.e.$, $a,\,ar,\,a{r^2}$
$a + ar + a{r^2} = 38$ and ${a^3}{r^3} = 1728$ ..$(i)$
$a(1 + r + {r^2}) = 38$ ..$(ii)$
From equation $(i)$, $ar = 12$
==> $a = \frac{{12}}{r}$
From equation $(ii)$ $\frac{{12}}{r}(1 + r + {r^2}) = 38$
on solving $r = 2/3$ and $a = \frac{{12 \times 3}}{2} = 18$
Required number $18, 12, 8$
Maximum number $i.e.$, $18.$
Standard 11
Mathematics
