# 6.1 Sequences and Arithmetic Sequences 3/20/2013

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5.1 Pascals Triangle and Binomial Theorem

6.1 Sequences and Arithmetic Sequences3/20/2013Sequencea list of terms with a particular order.Ex. 2, 5, 8, 11, 14, (increasing by 3)or 2, 5, 10, 17, 26, (increasing by 3, 5, 7, 9, etc)If the terms of a sequence have a recognizable pattern, you may be able to write a rule for the nth term of the sequence.Find the pattern by writing an expression (or rule) for the nth term:Or Find the pattern by writing an expression (or rule) for the nth term:Write the first five terms of the following sequences:Write the first five terms of the following sequences:Arithmetic SequencesDetermine whether the sequence is arithmeticYes

Yes

NoRule for finding the nth term of arithmetic sequence:The story is told of a grade school teacher In the 1700's that wanted to keep her class busy while she graded papers so she asked them to add up all of the numbers from 1 to 100. These numbers are an arithmetic sequence with common difference 1. Carl Friedrich Gauss was in the class and had the answer in a minute or two (remember no calculators in those days). This is what he did:1 + 2 + 3 + 4 + 5 + . . . + 96 + 97 + 98 + 99 + 100sum is 101sum is 101With 100 numbers there are 50 pairs that add up to 101. 50(101) = 5050

Sum of a finite Arithmetic SeriesFind the sum of the arithmetic sequence:Find the sum of the HomeworkWorksheet 6.1 odd problems only.

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