MATH
Give at least 5 examples of infinite geometric series satisfying this following conditions
refer to picture below)
Answers
Given : Geometric series
limiting sum = 5
common ratio negative
first term not a prime number
To Find : 5 examples of infinite geometric series satisfying given conditions
Solution:
geometric sequence
a , ar , ar² ...
a = first term
r = common ratio
Sum of infinite series = a/(1 - r)
a = first term
r = common ration
-1 < r < 0 as r is negative
Sum = 5
a/(1 - r) = 5
r = -1/2
=> a/(1 - (-1/2)) = 5
=> a = 15/2
r = -1/3
=> a/(1 - (-1/3)) = 5
=> a = 20/3
r = -1/4
=> a/(1 - (-1/4)) = 5
=> a = 25/4
r = -1/5
=> a/(1 - (-1/5)) = 5
=> a = 6
r = -1/6
=> a/(1 - (-1/6)) = 5
=> a = 35/6
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Step-by-step explanation:
geometric sequence
a, ar, ar²...
a = first term
r = common ratio
Sum of infinite series = a/(1-r)
a = first term
r = common ration
-1 <r <0 as r is negative
Sum = 5
a/(1-r) = 5
r = -1/2
=> a/(1- (-1/2)) = 5
=> a = 15/2
r = -1/3
=> a/(1-(-1/3)) = 5
=> a = 20/3.
r = -1/4
=> a/(1- (-1/4)) = 5
=> a = 25/4
r = -1/5
=> a/(1-(-1/5)) = 5
=> a = 6
r = -1/6
=> a/(1- (-1/6)) = 5
=> a = 35/6.