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Pre-Calculus 12 Test On-Line Course 5. Determine the first term for the arithmetic sequence given the following values: t33 = 92, d = -2. A. 159 B. 215 C. 218 D. 156 5. 6. What position is the term 5- in the arithmetic sequence 9- , 9, 8 , ..., 5-? A. 4 B. 16 C. 14 D. None of the above options 6. 7. What is 12 if to = 12 and t20 = 36 ? A. 18 15 C. 24 D. 20 7. 8. What is the common difference (d) if t, = -14 and to = -32? A. -18 B. 3 C. -3 D. 6 8. Version 1 2019 Page 3 of 10 Test Pre-Calculus 12 Test On-Line Course6 of 10 Pre-Calculus 12 Test On-Line Course 16. The first three terms of a geometric sequence are m, m+3, and m+7. Determine the numerical value of the first three terms. A. 5, 8, 12 B. 9, 12, 16 C. 7, 10, 14 D. 8, 11, 15 16. 17. A geometric sequence has the terms 3, 15, 75, ..., if the sum of the first n terms is 3(1 - 57) Sn = 1 -5 Determine the value of n. A. 3 B. 4 C. 5 D. 7 17 . 18. If the sum of the first 6 terms of a geometric series is 1456 and the common ratio is 3, determine the value of the first term. A. B. 4 C. 2912 D. 728 18. 19. If the sum of an infinite geometric series is 6 and the first term is 8, determine the common ratio. A. B. C. A/W D. 19. Version 1 2019 Page 6 of 10 Test Pre-Calculus 12 Test On-Line Course 20. A ball is dropped from a nergm s to 75% of i8 of 10 Pre-Calculus 12 Test On-Line Course 24. The pH scale measures the acidity or the alkalinity of a solution. A difference of one unit of pH represents a tenfold increase in acidity or alkalinity. Normal rain has a pH of 5 and sea water has a pH of 9. If normal rain is more acidic than sea water, then how many times is it more acidic? A. 4 times B. 10 000 times C. 4 000 times D. 40 times 24. 25. Determine the first term in the expansion of _ 3(2* ). A. 3 B. 6 C. 12 D. 36 25 26. Determine the sum of the infinite geometric series: _ 200(0.6)k-1 K=1 A. 125 B. 333 C. 500 D. no finite sum 26. Version 1 2019 Page 8 of 10 Test Pre-Calculus 12 Test On-Line CourseVersion 1 2019 Page 4 of 10 Test 5 of 10 Pre-Calculus 12 Test On-Line Course 12. Determine the 11th term in the geometric sequence 15, -9, 27 5 ' .... A. -45 B. -0.0907 C. 0.0907 D. -0.0544 12. 13. How many terms are in the geometric sequence 24, 72, 216, ...., 4 251 528? A. 15 B. 13 C. 12 D. 11 13 14. In the sequence in question 13, what term is 52488? A. 10th B. 1094th C. 7th D. 8th 14. 15. Given a geometric sequence with t, =-128 and t, = 1024, determine the first 3 terms of the sequence. A. -16, 32, -64 , ... B. -16, -32 , -64 , ... C. 16, -32, 64, ... D. 16, 32, 64 , ... 15. Version 1 2019 Page 5 of 10 Test9 of 10 Pre-Calculus 12 Test On-Line Course PART B WRITTEN RESPONSE (show all work for full marks) 1. The local store makes a display of soup that is in the shape of a triangle. There are 20 cans in the 5th row from the top and 68 cans in the 17th row from the top. a) How many cans are in top row? a) 3 marks b) Write a general term for this arithmetic sequence. b ) 2 marks 2. The sum of the first three terms in an arithmetic series is -6 and the product of these terms is 24. Find the first three terms. 2. 3 marks Version 1 2019 Page 9 of 10 Test Pre-Calculus 12 Test On-Line CourseVersion 1 2019 Page 9 of 10 Test 10 of 10 Pre-Calculus 12 Test OnLine Course 3. In a geometric sequence t3 = 9000 and t6 : 15 552. Find the rst term. 3. 3 marks 10 3 k *1 4. Evaluate and show formula used. 2 64[] k=3 4 4. 3 marks Version 1 2019 Page 100f 10 Test 7 of 10 Version 1 2019 Page 6 of 10 Test Pros-Calculus 12 Test OnLine Course 20. A ball is dropped from a height of 16 m, After each bounce the ball rises to 75% of its previous height. Determine the total vertical distance the ball travels before coming to rest. A. 64 B. 108 C. 112 D. 128 20. 21. The brightness of direct sunlight that passes through a sheet of glass is reduced by 10%. Determine an expression for the percent of the original brightness of sunlight left after it passes through 6 sheets of glass. A. 100(0.9)6 B. 1000.1)6 C. 100(0.9)5 D. 1000.1)5 21. 22. A population of insects can double in 25 days. After 60 days, how many times greater will the population be than after 25 days? A. 5.28 times B. 3.03 times C. 2.40 times D. 2.64 times 22. 23. For each increase of 1 unit in magnitude of an earthquake, there is a tenfold increase in the amount of energy released. An earthquake in Turkey was measured with a magnitude of 2.7. An earthquake occurred 1 day later in Japan and measured 7.1 in magnitude. About how many times more powerful is the earthquake in Japan than in Turkey? A. 398 times B. 2.4 times C. 25 ll9times D. 2.6 times 23. Version 1 2019 Page 7 of 10 Test 4 of 10 Pre-Calculus 12 Test On-Line Course 9. What is the sum of the first 15 terms of an arithmetic series if a = 1 1 and t, = 130 A. 109 B. 900 C. 1269 D. 1057.5 9 . 10. The sum of the first 5 terms of an arithmetic series is 30. The sum for the first 1 1 terms is 99. What are the first four terms of the series? A. 4, 5, 6, 7 B. 2, 4, 6, 8 C. 3, 5, 7, 9 D. -1, 4, 9, 14 10. 11. Determine the general term t, of a geometric sequence 18, 6, 2, .... A. 18 - 1 \\" -1 B. 18x 1 )" -1 C. (6 ) "-1 D. 18 1) 11. Version 1 2019 Page 4 of 10 Test Pre-Calculus 12 Test On-Line CoursePre-Calculus 12 Test On-Line Course Pre-Calculus 12 Unit 8 Arithmetic & Geometric Sequence & Series Test Name Multiple Choice Section 26 Written Response Section 14 Total % 40 FORMULAE In = a+(n-1)d & _ "[ za+("-)doRS - 2 +(n-1)d] 2 2 tn = arn-1 S, = all-r") a-rl 1-r 1 - 1 Version 1 2019 Page 1 of 10 Test Pre-Calculus 12 Test On-Line Course20f'lO PreCalculus 12 Test OnLine Course PART A MULTIPLE CHOICE (1 mark each) 1. Which of the following sequences is NOT an arithmetic sequence? A. 8, 6, 4 , 2 B. 11, 7, 3, 1 C. 3, 6, 9 , 12 D. 0.75, 4, 7.25, 10.5 1. 2. Given the arithmetic sequence 2, 7, 716, 728, ..., determine the general term tn. A. 9}: 11 B. 9n 737 C. 1191: D. 199n 2. 3. In the arithmetic sequence in question 2 above, determine the 31St term. A. 298 B. 242 C. 268 D. 268 3. 4. Given the arithmetic sequence 43 , 32 , 21 , ..., 789 , determine the number ofterms in the sequence. A. 66 B. 13 C. 12 D. 43 4. Version 1 2019 Page 2 of 10 Test PreCalculus 12 Test OnLine Course