EXAMPLE 5

1. ( ) 8 + 103 2 S20 = 20 The correct answer is C. ANSWER EXAMPLE 5 Standardized Test Practice SOLUTION a1= 3 + 5(1) = 8 Identify first term. a20= 3 + 5(20) =103 Identify last term. Write rule for S20, substituting 8 for a1 and 103 for a20. = 1110 Simplify.

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

3. a. 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: EXAMPLE 6 Use an arithmetic sequence and series in real life SOLUTION an= a1 + (n – 1) = d Write general rule. = 3 + (n – 1)3 Substitute 3 for a1 and 3 for d. = 3n Simplify.

4. ( ) ( ) a1 + a14 3 + 42 Total number of cards = S14 = 14 = 14 = 315 2 2 EXAMPLE 6 Use an arithmetic sequence and series in real life SOLUTION Find the sum of an arithmetic series with first term a1 = 3 and last term a14 = 3(14) = 42. b.

5. S12 = 570 ANSWER for Examples 5 and 6 GUIDED PRACTICE 12 5. Find the sum of the arithmetic series (2 + 7i). i = 1 6. WHAT IF?In Example6,what is the total number of cards if the house of cards has 8 rows? ANSWER 108cards