sequences

sequences - r , called the common ratio , such that a n =...

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11.2 - Arithmetic Sequences A sequence of numbers a 1 , a 2 , a 3 , , a n , is called an arithmetic sequence if there is a constant d , called the common difference , such that a n = a n 1 + d , for every n > 1. Solving for d : d = a n a n 1 The nth term of an Arithmetic Sequence is: a n = a 1 + ( n 1) d , with a 1 =first term; d=common difference. The sum of the first n terms of an Arithmetic Sequence is: S n = n 2 ( a 1 + a n ) or, in alternate form, S n = n 2 (2 a 1 + ( n 1) d ) ___________________________________________________________ 11.3 - Geometric Sequences A sequence of numbers a 1 , a 2 , a 3 , , a n , is called a geometric sequence if there is a constant
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Unformatted text preview: r , called the common ratio , such that a n = ra n-1 , for every n > 1, r . Solving for r : r = a n a n 1 The nth term of a geometric sequence is: a n =a 1 r n-1 , where a 1 =first term; r=common ratio. The Sum of the First N Terms of a Geometric Sequence is: S N = a 1 r N 1 r , r 0,1 where a = first term, r = common ratio. The Sum of an Infinite Geometric Series S = ar k 1 k = 1 with common ratio |r|<1 is: S = a 1 r , where a = first term, r = common ratio....
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