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Series: Geometric Progression Formula Manipulation
If the sum of all the terms of an infinite geometric series starting at
1
---
7
 is
5
---
21
 then
the common ratio of the series must be

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 r:
r = 1 –
a
---
S
From the data above, a =
1
---
7
 and S =
5
---
21
:
r = 1 –
1
---
7
/
5
---
21
 = 1 –
1
---
7
×
21
---
5
 =
2
---
5
 = 0.4 to 3 dps.

© MEI Produced by Dr Ron Knott, revised 12 November 2007
tom . button [AT] mei . org . uk 		Test reference: SeriesGPFormula.html?ref=86239