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