What is the sum of the first six terms of the series? 40−10+2.5−0.625+... What is the answer as a simplified fraction

glamrockqueen7 2020-12-09 Answered
What is the sum of the first six terms of the series?
4010+2.50.625+...
What is the answer as a simplified fraction
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Expert Answer

odgovoreh
Answered 2020-12-10 Author has 107 answers
Given Data:
Series: 4010+2.50.625+...
The first term of series is: a=40
The second term of series is: a2=10
The third term of series is: a3=2.5
For the first and second term,
The common ratio of the series is,
r=a2a
Substitute the values in the above equation.
r=1040
=0.25
For the second and third term
The common ratio of the series is,
r=a3a2
Substitute the values in the above equation.
r=2.510
=0.25
So, the given series is a geometric series.
The sum of the first six terms of the geometric series is,
S6=a(1r6)(1r)
Substitute the values in the above equation.
S6=(40)(1(0.25)6)(1(0.25))
=40(0.9998)1.25
=31.99
Thus, the sum of the first six terms of the given geometric series is 31.99.
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Jeffrey Jordon
Answered 2021-12-27 Author has 2047 answers

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