Answer:
The sum to infinite = 7.5
Step-by-step explanation:
Lets revise the geometric sequence
- There is a constant ratio between each two consecutive numbers
Ex:
5 , 10 , 20 , 40 , 80 , ………………………. (×2)
5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Progression:
∵ U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
∴ Un = a(r^n-1), where a is the first term , r is the constant ratio
between each two consecutive terms and n is the position
of the term in the sequence
* The sum of first n terms of a Geometric Progression is calculate
from Sn = [a(1 - r^n)]/(1 - r)
* The sum to infinity of a Geometric Progression is:
S∞ = a/(1 - r), where -1 < r < 1
* In the problem a = 5 and r = 1/3
∵ a = 5 and r = 1/3
∵ S∞ = a/(1 - r)
∴ S∞ = 5/(1 - 1/3) = 5/(2/3) = 15/2 = 7.5
