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

Answer

d

Explanation

` :' ` Sum of infinite geometric series , ` S_(oo) = a/(1-r)`
`rArr 4 = a/(1-r)rArr a = 4- 4r " "` …(i)
Also, `T_(2) =ar rArr ar = 3/4 " "` …(ii)
Also , `T_(2)= ar = 3/4 `
From Eqs , (i) and (ii) ,we get
` a= 4 -4 (3/(4a))`
` rArr a= 4 - 3/a`
` rArr a^(2) - 4a +3 = 0`
` rArr a^(2) -3a +3 =0`
` rArr a(a-3) -1(a-3) = 0`
` rArr a = 1,3`
On putting a =3 in Eq. (ii) , we get
` 3r = 3/4 rArr r = 1/4`