# Geometric Series

C2 revision of key formulae and proofs needed for exam

- Created by: Olivia
- Created on: 04-04-11 19:23

First 173 words of the document:

GEOMETRIC SERIES

In GEOMETRIC SERIES each term is found by multiplying the previous term by a fixed

amount as opposed to arithmetic series whereby a fixed amount is added each time.

The common ratio , the amount which we multiply by is r .

The first term like in arithmetic series is denoted by a.

If r is more than 1 then each term will increase.

If r is a decimal number between 0 and 1 then each term of the sequence will

decrease

If r is a negative number each term will alternate between being negative and

positive.

The second formula is useful to avoid negatives.

To work out the sum to infinity this formula is used

Eg question WJEC C2 January 2008 question 4 A geometric series

has first term and common ratio . The fifth term of the geometric series is and the eighth term is . (a)

Show that and find the value . [5] (b) Find the sum to infinity of the series

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