1067 11.3 Geometric Sequences and Series Sn = a111 - r n2 1 - r Formula for Sn S4 = 100031 - 11.02244 1 - 1.02 Substitute. S4 ≈4121.61 Evaluate. The future value of the annuity is $4121.61. S Now Try Exercise 81. Future Value of an Annuity The formula for the future value of an annuity is given by the following. S =R c 1 1 +i2n −1 i d Here S is future value, R is payment at the end of each period, i is interest rate per period, and n is number of periods. 11.3 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. In a geometric sequence, each term after the first is obtained by multiplying the preceding term by a fixed nonzero real number called the common . 2. The common ratio for the sequence -25, 5, -1, 1 5 , c is . 3. For the geometric sequence having a1 = 6 and r = 2, the term a3 = . 4. For the geometric sequence with nth term an = 4 A 1 2B n-1 , the term a5 = . 5. The sum of the first five terms of the geometric sequence 5, 10, 20, 40, c is . 6. When evaluated, a 5 i=1 81 A1 3B i-1 is . CONCEPT PREVIEW Determine whether each sequence is arithmetic, geometric, or neither. If it is arithmetic, give the common difference d. If it is geometric, give the common ratio r. 7. 4, -8, 16, -32, c 8. 1 3 , 2 3 , 3 3 , 4 3 , c 9. 5, 10, 20, 35, . . . 10. 8, 2, 1 2 , 1 8 , c Recall from the beginning of this section that an employee agreed to work for the following salary: $0.01 the first day, $0.02 the second day, $0.04 the third day, $0.08 the fourth day, and so on, with wages doubling each day. Determine (a) the amount earned on the day indicated and (b) the total amount earned altogether after wages are paid on the day indicated. See Examples 1 and 5. 11. day 10 12. day 12 13. day 15 14. day 18
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