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Series: Geometric Progression Formula Manipulation
If the sum of all the terms of an infinite geometric series with common ratio
– 4
---
5
 is
35
---
72
then the first term of the series is

tickcross


Worked Solution:

The sum, S of all the terms of a geometric series
starting at a with common ratio r where –1 < r < 1 is given by S =
a
---
1 – r
The question asks for a:
a = S (1 – r)
For this series:
a =
35
---
72
 (1 –
– 4
---
5
)
=>a =
7
---
8
 = 0.875 to 3 dps.

© MEI Produced by Dr Ron Knott, revised 12 November 2007
tom . button [AT] mei . org . uk 		Test reference: SeriesGPFormula.html?ref=75416,qu=infa