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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 Winter '11
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 Calculus, 1 k, 1 k

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