Q. In a GP the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number the series becomes AP, then the greatest number is
A) 8
B) 4
C) 24
D) 16
Explanation
(a)
Let three numbers in GP are $\frac{a}{r},\ a,ar.$
From the given condition
$\frac{a}{r} + a + ar = 14\ \Rightarrow a\left( \frac{1}{r} + 1 + r \right) = 14\$ …(i)
and $\frac{a}{r} + 1,\ a + 1$ and $ar - 1 = \frac{a}{r}(1 + r^{2})$ …(ii)
From Eqs. (i) and (ii), we get
$a = 4$ and $r = 2$
So, required numbers are 2, 4, 8
Hence, greatest number is 8
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.