6.1 Sequences and Arithmetic Sequences 3/20/2013.

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Presentation transcript:

6.1 Sequences and Arithmetic Sequences 3/20/2013

Sequence a 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:

Arithmetic Sequences

Determine whether the sequence is arithmetic Yes No

Rule 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: sum is 101 With 100 numbers there are 50 pairs that add up to (101) = 5050

Sum of a finite Arithmetic Series

Find the sum of the arithmetic sequence:

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Homework Worksheet 6.1 odd problems only. “I tried to catch some fog. I mist!”