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1.3 Arithmetic Sequences

# 1.3 Arithmetic Sequences - Arithmetic Sequences Arithmetic...

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Unformatted text preview: Arithmetic Sequences Arithmetic Sequences Section 1.3 Arithmetic sequence – a sequence in which the difference between each term and the preceding term is always constant { 14, 10, 6, 2, ____, ____,…} {3, 5, 8, 12, ___, ___,…} In an arithmetic sequence { un } un = un −1 + d for some constant d and all n > 2. In an arithmetic sequence with { un } common difference d, un = u1 + (n − 1)d for every n > 1 Summation Notation Summation Notation m ∑c k =1 k = c1 + c2 + c3 + ... + cm Partial Sums of an Arithmetic Partial Sums of an Arithmetic Sequence { un } If is an arithmetic sequence with common difference d, then for each positive integer k, the kth partial sum can be found by using either of the following formulas. k k 1. ∑ un = ( u1 + un ) 2 n =1 k (k − 1) 2. ∑ un = ku1 + d 2 n =1 k Joke Time Joke Time What is an insect that’s not feeling well? Secant (sick ant) Who was a famous person that Who was a famous person that was not very healthy? “I sick” Newton ...
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