1047 11.1 Sequences and Series NOTE It is possible to evaluate the sums in Examples 6 and 7 without using the summation properties and rules; however, this can be tedious. EXAMPLE 7 Using the Summation Properties and Rules Evaluate a 6 i=1 1i2 + 3i + 52. SOLUTION a6 i=1 1i2 + 3i + 52 = a 6 i=1 i2 + a 6 i=1 3i + a 6 i=1 5 Property (c) = a 6 i=1 i2 + 3 a 6 i=1 i + a 6 i=1 5 Property (b) = a 6 i=1 i2 + 3 a 6 i=1 i + 6152 Property (a) = 616 + 12 12 # 6 + 12 6 + 3c 616 + 12 2 d + 6152 Summation rules = 91 + 63 + 30 Simplify. = 184 Add. S Now Try Exercise 81. 11.1 Exercises CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. 1. A(n) is a function that computes an ordered list. 2. A(n) sequence is a function that has the set of natural numbers of the form 51, 2, 3, c , n6 as its domain. 3. Some sequences are defined by a(n) definition, one in which each term after the first term or the first few terms is defined as an expression involving the previous term or terms. 4. The sum of the terms of a sequence is a(n) . It is written using the Greek capital letter symbol to indicate a sum. CONCEPT PREVIEW Answer each of the following. 5. Complete a table of values for the sequence an = 5n + 2 using n = 1, 2, 3, 4, 5. 6. Graph the sequence an = 5n + 2 using the values from Exercise 5. 7. Evaluate a 5 i=115i + 22. 8. Find the first five terms of the sequence defined by the following recursive definition. How is the sequence related to the sequence in Exercise 5? a1 = 7 an = an-1 + 5, if n 71
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