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