There are 8 terms of the series required to give the given sum
Step-by-step explanation:
The formula of the sum of n terms of a geometric series is
,where
- a is the first term in the series
- r is the common ratio between each two consecutive terms
∵ The series is 125 + 25 + 5 + 1 + ............
∵
∵
- There is a common ratio between each two consecutive terms
∴ The series is a geometric series, where a = 125 and r =
∵
∵ a = 125 , r = and
- Substitute these values in the rule above
∴
∴
∵
∴
- Divide both sides by
∴
- Subtract 1 from both sides
∴
- Multiply both sides by -1
∴
- Insert ㏑ in both sides
∴ ㏑ = ㏑
- Remember ㏑ = n ㏑(a)
∴ ㏑ = n ㏑
- Divide both sides by ㏑ to find n
∴ n = 8
There are 8 terms of the series required to give the given sum
Learn more:
You can learn more about the geometric series in brainly.com/question/1522572
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