Sequences and Series

3

3.1 Introduction EMCN

In this chapter we extendthe arithmetic and quadratic sequences studied inearlier grades, to geometric

sequences. We also look at series, which are the summing of the termsin sequences.

See introductory video:VMgjm at http://www.everythingmaths.co.za

3.2 Arithmetic Sequences EMCO

The simplest type of numerical sequence is an arithmetic sequence.

DEFINITION: Arithmetic Sequence

An arithmetic (or linear) sequence is a sequence of numbers in which each new term

is calculated by adding a constant value to theprevious term

For example,

1; 2; 3; 4; 5; 6;...

is an arithmetic sequence because you add 1 to the current term to get the next term:

first term: 1

second term: 2 = 1 + 1

third term: 3 = 2 + 1

..

.

nthterm: n = (n− 1) + 1

Activity: Common Difference

Find the constant valuethat is added to get the following sequences andwrite out the next

5 terms.

1. 2; 6; 10; 14; 18; 22;...
   2.−5;− 3;− 1; 1; 3;...


2. 1; 4; 7; 10; 13; 16;...
   4.−1; 10; 21; 32; 43; 54;...