Question

Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first 4 terms of the series

Answer 1

Answer with Explanation:

It is given that infinite geometric series with a beginning value of 2 , converges to 10.

Let a be the common ratio of geometric series.Where ,a<1.

Sum to infinity of a geometric series

`(a)/(1-r) for, r<1 or (a)/(r-1), for r>1.`

`2+2a+2a^2+2a^3+2a^4+.............{\text{to infinity}}=10\\\\ (2)/(1-a)=10\\\\ 1-a=(2)/(10)\\\\ 1-(1)/(5)=a\\\\a=(4)/(5)`

First four terms of geometric series

`2, 2*(4)/(5),2*((4)/(5))^2,2*((4)/(5))^3,2*((4)/(5))^4.\\\\2, (8)/(5),(32)/(25),(128)/(125),(512)/(625)`