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Unformatted text preview: Section 11.2 Arithmetic sequences An arithmetic sequence { a n } is a sequence that satisfies the following a 1 = a a n = a n 1 + d Example. The sequence { 2 , 5 , 8 , 11 , 14 , } is an arithmetic sequence with a 1 = 2 and d = 3. Example. Show that the sequence { a n } = { 2 n + 2 } is an arithmetic sequence. Solution. The difference between a n +1 and a n is d = a n +1 a n = (2( n + 1) + 2) (2 n + 2) = 2 is constant. Thus { a n } is an arithmetic sequence with a 1 = 4 and d = 2. Finding the nth term of an arithmetic sequence: a 1 = a a 2 = a + d a 3 = a + 2 d a n = a + ( n 1) d The above shows that the nth term of an arithmetic sequence is a n = a + ( n 1) d Example. Find the fifth term of a sequence if the 14th term is 97 and the common difference is 3. Solution. a n = a +( n 1) d implies 97 = a 1 +(13)(3). Thus, a 1 = 58 and a 5 = a 1 +4 d = 58+4(3) = 70....
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 Fall '11
 Kutter
 Algebra

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