Question

In a G.P. the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number, the series becomes A.P., then the greatest number is

• A. 8
• B. 4
• C. 24
• D. 16

Answer 1

The correct option is A 8

Let three numbers in G.P. are $\frac{a}{r},a,ar.$
Condition I: $\frac{a}{r}+a+ar=14\Rightarrow a(\frac{1}{r}+1+r)=14$ .......(i)
Condition II: $\frac{a}{r}+1,a+1$ and $ar-1$ will be in A.P.,
then $\frac{a}{r}+1,a+1$ and $ar-1$ .......(ii)
From (i) and (ii), we get a = 4 and r = 2.
So, required numbers are 2, 4, 8.
Hence greatest number is 8.