1058 CHAPTER 11 Further Topics in Algebra CONCEPT PREVIEW Evaluate each sum. 9. a 5 i=114i - 12 10. S10 for the sequence 5, 10, 15, 20, . . . CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. In an arithmetic sequence, each term after the first differs from the preceding term by a fixed constant called the common . 2. The common difference for the sequence -25, -21, -17, -13, c is . 3. For the arithmetic sequence having a1 = 10 and d = -2, the term a3 = . 4. For the arithmetic sequence with nth term an = 8n + 5, the term a5 = . Determine the common difference d for each arithmetic sequence. See Example 1. 11. 2, 5, 8, 11, c 12. 4, 10, 16, 22, c 13. 3, -2, -7, -12, c 14. -8, -12, -16, -20, c 15. x + 3y, 2x + 5y, 3x + 7y, c 16. t2 + q, -4t2 + 2q, -9t2 + 3q, c Find the first five terms of each arithmetic sequence. See Example 2. 17. The first term is 8, and the common difference is 6. 18. The first term is -2, and the common difference is 12. 19. a1 = 5, d = -2 20. a1 = 4, d = 3 21. a1 = 10 + 27, a2 = 10 22. a1 = 3 - 22 , a2 = 3 11.2 Exercises Determine an and a8 for each arithmetic sequence. See Examples 3 and 4. 23. 5, 7, 9, c 24. -3, -7, -11, c 25. a1 = 5, a4 = 15 26. a1 = -4, a5 = 16 27. a10 = 6, a11 = 10.5 28. a15 = 8, a16 = 5 29. a1 = x, a2 = x + 3 30. a2 = y + 1, d = -3 31. a4 = s + 6p, d = 2p 32. a3 = z - 8w, d = -4w CONCEPT PREVIEW The figure shows the graph of a finite arithmetic sequence. 5. Determine the domain and range of the sequence. 6. What is the first term? 7. What is the common difference? 8. Write a formula for the nth term of the sequence. 1 3 5 –4 0 4 8 n an
RkJQdWJsaXNoZXIy NjM5ODQ=