Answer:
40 + 20 + 10 + 5 is a geometric series
Explanation:
* Lets revise the geometric series
- 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 Series:
∵ U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
∴ Un = ar^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 series
* Now lets check the answers to find the correct one
# 40 + 50 + 60 + 70
∵ 50/40 = 5/4
∵ 60/50 = 6/5
∵ 5/4 ≠ 6/5
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 42 + 44 + 46
∵ 42/40 = 21/20
∵ 44/42 = 22/21
∵ 21/20 ≠ 22/21
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 80 + 40 + 120
∵ 80/40 = 2
∵ 40/80 = 1/2
∵ 2 ≠ 1/2
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 20 + 10 + 5
∵ 20/40 = 1/2
∵ 10/20 = 1/2
∵ 5/10 = 1/2
- There is a common ratio between each two consecutive terms
∴ 40 + 20 + 10 + 5 is a geometric series