To what sum does the geometric series `2.8+2.1+1.575+….` converge ?

Options

A. `3.73`
B. `4.97`
C. `6.47`
D. `11.20`

Answer

D

Explanation

You can use the formula `S_(oo)=(a_(1))/(1-r)` to find the sum that an infinite geometric series converges to, where `a_(1)` is the first term and r is the ratio of one term to the previous term.
Here, `a_(1)=2.8` and `r=(2.1)/(2.8)=0.75`.
`S_(oo)=(a_(1))/(1-r)=(2.8)/(1-0.75)=(2.8)/(0.25)=11.2`
So the sum that this infinite series converges to is 11.2.