NIDES Precalculus 12 Show ALL work for full marks. I encourage you to write out the formula FIRST then substitute. 3. What are the similarities and differences between of an arithmetic sequence and a series? (2 marks) Determine the indicated term of the arithmetic sequence. -3,2,7, 12, .... 20 .coneupse allsmiths nevis ord nal fio bally one 18 12. Find the sum of the first 23 terms in the 5. Given the arithmetic sequence 4, -10, -24, -38 a) determine the general term t. someupse sri to armof owl nevin sonswipes bitsmonths an hot mhed basalbal ed) animeted ? e Yeshem S) b) determine the 24th term. Unit 5 3 of 10NIDES Precalculus 12 6. Given the arithmetic sequence: -11, -5, 1, ..., 175. Determine the number of terms in the sequence. an 7. Determine the first term for the arithmetic sequence given the following values. t43 = -188, d = -7 8. What position is the given term (find n ) for the given arithmetic sequence. tn = -1 in the sequence of: 7,62, 63, navia 9. Determine the indicated term for an arithmetic sequence given two terms of the sequence. t5 = 39, t23 = 156; determine t16 (2 marks) Unit 5 4 of 10NIDES Precalculus 12 10. An arithmetic sequence has seven terms. Given the first term in the sequence is 7, and the last term is 26.5, determine the missing terms. 11. An arithmetic sequence has the following terms. Determine the arithmetic mean and then determine an expression for the common difference: 2x + 3, ,8x - 5 12. Find the sum of the first 23 terms in the following series. 3+7+11+15 + .... 13. Determine the sum of the following arithmetic series: (2 marks) -13 -10-7-...+ 62 Determine the Unit 5 5 of 10NIDES Precalculus 12 14. Determine the common difference, d for the arithmetic series given the following values. Sil = 682 and a = 17 15. Determine the arithmetic series that has these partial sums: (2 marks) $4 = 26, S5 = 40, and 56 = 57 16. Use the given date about each arithmetic series to determine the indicated value. a) S17 = 106.25 and t17 = 8.25; determine a b) S15 = 337.5 and a = -2; determined Unit 5 6 of 10NIDES Precalculus 12 All answers rounded to 2 decimal places unless otherwise stated. 17. Given the geometric sequence: 4, 10, 25, ... a) determine the general term In . b) determine the 9th term. 18. In a geometric sequence t4 = 189 and t7 = 5103. Find the first three terms. (2 marks) Determine the Free 19. Given a geometric sequence with t3 = 625 and to = -78125, determine the first term. (2 marks) 20. The following three terms y - 6, y, y + 9 form a geometric sequence. Determine the value of y. Unit 5 7 of 10NIDES Precalculus 12 21. A racquet ball drops from a height of 7 metres. After each bounce it rises to a height that is 64% of the previous height. a) Write the general term of the sequence that relates the height of the bounce to the number of bounces. b) What height does the ball reach after the 7th bounce? 22. Given the geometric series: 3 - 12 + 48-. ... + 196608 a) determine the number of terms in the series. b) determine the sum. 23. Determine term 8 in the geometric sequence: 2x3, 6x4y2, 18x5y4, .... Unit 5 8 of 10NIDES Precalculus 12 24. If the sum of the first 7 terms of a geometric series is 8,744 and the common ratio is 3, determine the value of the first term. 25. Determine the value for x so that the following 3 terms form a geometric sequence: 3x 33-2x 9x-1 26. The sum of an infinite geometric series is and the common ratio is Determine the first term. 27. Determine the common ratio for each of the following geometric series. Calculate the sum where it exists. a) 5- 1+ - . .. b) + + 3 00 1 w + 16 9 of 10NIDES Precalculus 12 28. A hard rubber ball is dropped from a moving van with a height of 6 metres. The ball rises to 70% of the previous height after each bounce. Calculate the total vertical distance the ball travels before coming to rest. Round your answer to the nearest hundredth of a metre. (2 marks) 29. State the number of terms in each series: a) b) 35 [ 20-3 b + 15 [ 3 k - 7 a =9 k = b 30. Evaluate: (2 marks each) a) b) 11 E 16/ - 1 ) k - 1 K=2 [ 35 () Unit 5 10 of 10