If the sum to infinity of the series
`3+(3+d)1/4+(3+2d)1/4^(2)+..oo` is `44/9`, then find d.

Options

A. 9
B. 5
C. 1
D. none of these

Answer

A

Explanation

The given series is an arithmetico-geometric series.
We have,
`3+(1)/(4)(3+d)+(1)/(4^(2))(3+2d)+ . . . . "to "oo=8`
`rArr" "(3)/(1-1//4)+(d xx1//4)/((1-1//4)^(2))=8" "{:["Using":S=(a)/(1-r)+(dr)/((1-r)^(2))]:}`
`rArr" "4+(4d)/(9)=8rArrd=9`