SEQUENCES AND SERIES

In this chapter we extend the arithmetic and quadratic sequences studied in earlier grades, to geometric sequences. We also look at series, which are the summing of the terms in sequences.

Arethmetic Sequences

1). Arithmetic sequences

The simplest type of numerical sequence is an arithmetic sequence.

Definition 1: 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 the previous 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:

Table 1

first term: 1

second term: 2=1+1

third term: 3=2+1

⋮ nth term: n=(n−1)+1

Activity 1: Common difference Find the constant value that is added to get the following sequences and write out the next 5 terms.

1. 2; 6; 10; 14; 18; 22;…

2. −5; −3; −1; 1; 3;…

3. 1; 4; 7; 10; 13; 16;…

4. −1; 10; 21; 32; 43; 54;…

5. 3; 0;−3;−6;−9;−12;…

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