A) 8
B) 4
C) 24
D) 16
Correct Answer: A
Solution :
Let three numbers in G.P. are \[\frac{a}{r},\ a,\ ar\]. Condition I: \[\frac{a}{r}+a+ar=14\Rightarrow a\left( \frac{1}{r}+1+r \right)=14\] ?.(i) Condition II: \[\frac{a}{r}+1,\ a+1\] and \[ar-1\] will be in A.P., then \[2(a+1)=\frac{a}{r}+1+ar-1=\frac{a}{r}(1+{{r}^{2}})\] ......(ii) From (i) and (ii), we get \[a=4\] and \[r=2\]. So, required numbers are 2, 4, 8. Hence greatest number is 8.
You need to login to perform this action.
You will be redirected in
3 sec
