Arithmetic Sequences Arithmetic Sequences and Seriesand Series

A sequence is arithmetic if

each term – the previous term = d

where d is a constante.g. For the

sequence ...,8,6,4,2d = 2nd term – 1st

term= 3rd term – 2nd term . . . = 2

Arithmetic Sequence

The 1st term of an arithmetic sequence is

given the letter a.

Arithmetic Sequence

An arithmetic sequence is of the form...,3,2,, dadadaa

Notice that the 4th term has 3d added so, for example, the 20th term will be

da 19

The nth term of an Arithmetic Sequence is dnaun )1(

An arithmetic sequence is sometimes called an Arithmetic Progression (A.P.)

SUMMARY

)(2

lan

Sn

The sum of n terms of an arithmetic series

is given by

...,3,2,, dadadaa

An arithmetic sequence is of the form

The nth term is dnaun )1(

or

))1(2(2

dnan

Sn

ExampleThe common difference of an arithmetic series

is -3 and the sum of the first 30 terms is 255. Find the 1st term.

Solution:

255303 30S and , nd

))1(2(2

dnan

S n

))3(292(2

30255 a

)872(15255 a

87215

255 a

52 aa28717