Explanation Definition used: Infinite Sequence: An infinite sequence is denoted by { a n } , is a function whose domain is the set of positive integers. The functional values a 1 , a 2 , a 3 ⋯ , a n , ⋯ are the terms of the sequence and the term a n is called the n th term of the sequence. Calculation: Let { a n } = { 3 n 2 − n + 1 2 n 2 + 1 } . Find the first five terms of the sequence { a n } = { 3 n 2 − n + 1 2 n 2 + 1 } as follows. Substitute n = 1 in a n = 3 n 2 − n + 1 2 n 2 + 1 . a 1 = 3 ( 1 ) 2 − 1 + 1 2 ( 1 ) 2 + 1 = 3 + 0 2 + 1 = 3 3 = 1 Substitute n = 2 in a n = 3 n 2 − n + 1 2 n 2 + 1 . a 2 = 3 ( 2 ) 2 − 2 + 1 2 ( 2 ) 2 + 1 = 3 ( 4 ) − 1 2 ( 4 ) + 1 = 12 − 1 8 + 1 = 11 9 Substitute n = 3 in a n = 3 n 2 − n + 1 2 n 2 + 1

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Chapter 11.2, Problem 9E

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To write: The first five terms of the sequence {an}={3n2−n+12n2+1}.

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Chapter 11.2, Problem 8E

Chapter 11.2, Problem 10E

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The first five terms of the sequence { a n } = { 3 n 2 − n + 1 2 n 2 + 1 } .

Solution Summary: The author explains that an infinite sequence is denoted by lefta_nright, is a function whose domain is the set of positive integers.

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To write: The first five terms of the sequence {an}={3n2−n+12n2+1}.

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Chapter 11 Solutions