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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 ```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```
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