Sequences & Series

Number of sequeneses are set of numbers defined by a rule for positive integers.

This rule is called the general term (or “n # term”).

Sequences can be defined by

• Formula Un = 3n + 11

• A few words start at 14 and go up in three’s

• A list of terms 14, 17, 20, 23, 26, …….

The general Term is denoted:

Un, An, tn, Tn

A sequence defined by Un is denoted by

{Un} curly braces mean sequence

eg. {2n - 1} = 1, 3, 5, 7, 9, … , 2n – 1

Arithmetic Sequences

{Un} is an arithmetic sequence if successive terms have a common difference.

Un + 1 – Un = d Doesn’t mean +1 but the next term.

Eg. 1, 3, 5, 7, 9,….

Un = 5

Un + 1 – Un =d “d” is the common difference

d= 7

The general term of an arithemetic sequence:

Un = U1 + ( n – 1) – d

Eg If an arithemetic sequence has U7 = 17 and U12 = 29

Find U37

14 = U1 + (7 – 1) d → U1 + 6d = 14

29 = U1 + (12 – 1)d → U1 + 12d = 29

____________________

5d = 15

Geometric Sequence

{Un} is a geometric sequence if successive terms have a common ratio.

i.e. Un + 1 = r

Un

General term for a geometric sequense is given by:

Un = U1 x rn-1