1116 CHAPTER 11 Further Topics in Algebra Determine the indicated terms for each sequence described. 12. An arithmetic sequence has a5 = -3 and a15 = 17. Find a1 and an. 13. A geometric sequence has a1 = -8 and a7 = - 1 8 . Find a4 and an. Determine a8 for each arithmetic sequence. 14. a1 = 6, d = 2 15. a1 = 6x - 9, a2 = 5x + 1 Determine S12 for each arithmetic sequence. 16. a1 = 2, d = 3 17. a2 = 6, d = 10 Determine a5 for each geometric sequence. 18. a1 = -2, r = 3 19. a3 = 4, r = 1 5 Determine S4 for each geometric sequence. 20. a1 = 3, r = 2 21. a1 = -1, r = 3 22. 3 4 , - 1 2 , 1 3 , c Evaluate each sum that exists. 23. a 7 i=1 1-12i-1 24. a 5 i=1 1i2 + i2 25. a 4 i=1 i + 1 i 26. a10 j=1 13j - 42 27. a2500 j=1 j 28. a 5 i=1 4 # 2i 29. a ∞ i=1 a 4 7b i 30. a ∞ i=1 -2 a 6 5b i 31. a ∞ i=1 2 a- 2 3b i 32. Concept Check Find an infinite geometric series having common ratio 3 4 and sum 6. Evaluate each series that converges. Identify any that diverge. 33. 24 + 8 + 8 3 + 8 9 + g 34. - 3 4 + 1 2 - 1 3 + 2 9 - g 35. 1 12 + 1 6 + 1 3 + 2 3 + g 36. 0.9 + 0.09 + 0.009 + 0.0009 + g Evaluate each sum where x1 = 0, x2 = 1, x3 = 2, x4 = 3, x5 = 4, and x6 = 5. 37. a 4 i=1 1xi 2 - 62 38. a 6 i=1 ƒ1xi2 Δx; ƒ1x2 =1x -223, Δx =0.1 Write each sum using summation notation. 39. 4 - 1 - 6 - g- 66 40. 10 + 14 + 18 + g+ 86 41. 4 + 12 + 36 + g+ 972 42. 5 6 + 6 7 + 7 8 + g+ 12 13 Write the binomial expansion of each expression. 43. 1x + 2y24 44. 13z - 5w23 45. ¢32x - 12x≤ 5 46. 1m3 - m-224 Find the indicated term or terms of each expansion. 47. sixth term of 14x - y28 48. seventh term of 1m- 3n214 49. first four terms of 1x + 2212 50. last three terms of 12a + 5b216
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