Question

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

Answer 1

Correct Answer - A
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`