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EXAMPLE 5 Standardized Test Practice SOLUTION a 1 = 3 + 5(1) = 8 a 20 = 3 + 5(20) =103 S 20 = 20 ( ) 8 + 103 2 = 1110 Identify first term. Identify last term. Write rule for S 20, substituting 8 for a 1 and 103 for a 20. Simplify. ANSWER The correct answer is C.

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EXAMPLE 6 Use an arithmetic sequence and series in real life You are making a house of cards similar to the one shown Write a rule for the number of cards in the nth row if the top row is row 1. a. What is the total number of cards if the house of cards has 14 rows? b. House Of Cards

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EXAMPLE 6 Use an arithmetic sequence and series in real life SOLUTION Starting with the top row, the numbers of cards in the rows are 3, 6, 9, 12,.... These numbers form an arithmetic sequence with a first term of 3 and a common difference of 3. So, a rule for the sequence is: a. a n = a 1 + (n – 1) = d = 3 + (n – 1)3 = 3n Write general rule. Substitute 3 for a 1 and 3 for d. Simplify.

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EXAMPLE 6 Use an arithmetic sequence and series in real life SOLUTION Total number of cards = S 14 = 14 ( ) a 1 + a 14 2 = 14 ( ) 3 + 42 2 = 315 Find the sum of an arithmetic series with first term a 1 = 3 and last term a 14 = 3(14) = 42. b.

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GUIDED PRACTICE for Examples 5 and 6 5. Find the sum of the arithmetic series (2 + 7i). 12 i = 1 ANSWER S 12 = 570 6. WHAT IF? In Example 6, what is the total number of cards if the house of cards has 8 rows? ANSWER 108 cards

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