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