Let a,b ,c be positive integers such that `b/a` is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of `(a^2+a-14)/(a+1)` is

Answer

4

Explanation

According to the question
`b/a = c/b `=(integer)
`rArr b^2=ac rArr c = (b^2)/(a)`
Also given `(a+b+c)/(3)=b+2`
`rArr a+b+c = 3b +6`
`rArr a-2b+c =6`
`rArr a-2b+b^2/a=6`
`rArr 1-(2b)/(a)+(b^2)/(a^2)=6/a`
`rArr (b/a -1)^2=6/a`
` a=6 ` only
`rArr (a^2+a-14)/(a+1)=4`