consider an infinite geometric series with first term `a` and comman ratio `r` if the sum is `4` and the second term is `3/4` then find `a&r`

Options

A. `a = 4//7, r= 3//7`
B. `a = 2, r = 3//8`
C. `a = 3//2, r = 1//2`
D. `a = 3, r =1//4`

Answer

D

Explanation

Since, sum = 4 and second term `= (3)/(4)`
It is given first term a and common ratio r
`rArr (alpha)/(1-r) = 4, alphar = (3)/(4)`
`rArr r = (3)/(4alpha)`
`rArr (alpha)/(1 - (3)/(4 alpha)) = 4`
`rArr (4 alpha^(2))/(4alpha -3) = 4`
`rArr (alpha -1) (alpha -3) = 0`
`rArr alpha = 1 or 3`
When `alpha = 1, r = 3//4`
and when `alpha = 3, r = 1//4`