Answer:
the series is geometric and finite
Step-by-step explanation:
Given:
5, 10, 20, 40, 80, 160, 320
To find:
if the series is arithmetic or geometric; infinite or finite
a) For a series to be arithmetic, it must have a common difference
common difference = next term - previous term
For the series to be geometric, it must have a common ratio
common ratio = next term/previous term
We need to check if it has a common difference or common ratio
let next term = 10, previous term = 5
common difference = 10 - 5 = 5
let next term = 20, previous term = 10
common difference = 20 - 10 = 10
The difference is not common, it is different
common ratio = next term/previous term
let next term = 10, previous term = 5
common ratio = 10/5 = 2
let next term = 20, previous term = 10
common ratio = 20/10 = 2
The ratio is common
As a result, the series is geometric
b) Infinite series cannot be counted and totaled. This is because they do not end
Finite series can be counted and summed up. This is because the series has an end.
The series is finite