Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.

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Presentation transcript:

Arithmetic Sequences and Series

A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term – 1 st term = 3 rd term – 2 nd term... = 2 Arithmetic Sequence The 1 st term of an arithmetic sequence is given the letter a.

Arithmetic Sequence An arithmetic sequence is of the form Notice that the 4 th term has 3 d added so, for example, the 20 th term will be The n th term of an Arithmetic Sequence is An arithmetic sequence is sometimes called an Arithmetic Progression (A.P.)

SUMMARY  The sum of n terms of an arithmetic series is given by  An arithmetic sequence is of the form  The n th term is or

Example The common difference of an arithmetic series is - 3 and the sum of the first 30 terms is 255. Find the 1 st term. Solution: