11_2 - { a n } . Then S 1 = a 1 S 2 = a 1 + a 2 = a 1 + ( a...

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Section 11.2: Arithmetic Sequences Instructor: Ms. Hoa Nguyen (nguyen@scs.fsu.edu) 1 Arithmetic Sequences An arithmetic sequence { a n } satisfies the following: a 1 a n = a n - 1 + d where a 1 is the first term, d is the common difference. 2 Find the n -th term of an arithmetic sequence Given the first term a 1 and the common difference d : a 1 a 2 = a 1 + d a 3 = a 1 + 2 d ... a n = a 1 + ( n - 1) d So, the n -th term of an arithmetic sequence is: a n = a 1 + ( n - 1) d . Example 1 : Example 2 : 1
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Example 3 : Example 4 : Example 5 : 3 Summing the terms of arithmetic sequence Let S k ( k = 1 , ..., n ) be the sum of the first k terms of an arithmetic sequence
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Unformatted text preview: { a n } . Then S 1 = a 1 S 2 = a 1 + a 2 = a 1 + ( a 1 + d ) = 2 a 1 + d S 3 = a 1 + a 2 + a 3 = a 1 + ( a 1 + d ) + ( a 1 + 2 d ) = 3 a 1 + 3 d ... S n = a 1 + a 2 + a 3 + ... + a n = a 1 + ( a 1 + d ) + ( a 1 + 2 d ) + ... + [ a 1 + ( n-1) d ] = na 1 + [1 + 2 + ... + ( n-1)] d = na 1 + n ( n-1) 2 d Note: S n = na 1 + n ( n-1) 2 d = n 2 (2 a 1 + ( n-1) d ) = n a 1 + a n 2 So, S n = na 1 + n ( n-1) 2 d . Example 6 : 2...
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This note was uploaded on 05/23/2011 for the course MAC 1147 taught by Professor Nuegyen during the Spring '11 term at FSU.

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11_2 - { a n } . Then S 1 = a 1 S 2 = a 1 + a 2 = a 1 + ( a...

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