\fc) 4+69+.... r : I mark S = 2 marks . . . . . . 5 . . 4 23. The sum of an infinite geometric series 18 5 and the common ratio is . Find the first term. 23. 2 nmrks 24. A hard rubber ball is dropped from a moving van with a height of 5 metres. The ball rises to 80% of the previous height after each bounce. a) determine the total vertical distance the ball has traveled when it strikes the ground the eighth time. a) 3 marks Page 10 of 12 b) estimate the total vertical distance the ball travels before it comes to rest. b) 2 marks 25. For what values of x for the geometric series have a sum to infinity? 1 + 3x + 9x2 + 27x3 + 25. 2 marks 26. State the number of terms in each series. 33 a) 2 20-?! a :17 a) 1 nmrk b + 12 b) 3n 7 k=b b) I nmrk Page 11 of 12 \f1. Which of the following sequences is NOT an arithmetic sequence? A. 6, -2, -10, -18, ... B. 1, 2, 4, 8, 16, ... C. 1, 1, 14, 2, ... D. 5, 10, 15, 20, ... 1 . 2 marks 2. Determine the indicated term of the arithmetic sequence. -9, -5, -1, 3, ...; 34 2) 2 marks 3. Given the arithmetic sequence -38, - 47, - 56, - 65, ... a) determine the general term t . a) 2 marks b) determine the 25/ term. b ) 2 marks Page 2 of 124. Given the arithmetic sequence 19, 1 1, 3, ...., -477 . Determine the number of terms in the sequence. 4) 2 marks 5. Determine the first term for the arithmetic sequence given the following values. $27 = 87, d = -3 5) 2 marks 6. What position is the given term (find n ) for the given arithmetic sequence. 1 = - 20; 5, 5, 45,.. 6) 2 marks Page 3 of 12Determine the indicated term for an arithmetic sequence given two terms of the sequence. f4 = 18, f16 = 54;determme 2'10 7) 2 marks The unit measure for atmospheric pressure is kPa (Kilo-Pascals). At sea level the standard atmospheric pressure is 101.3 kPa. For every 1000 feet increase in altitude, atmospheric pressure decreases by 1.8 kPa. What is the atmospheric pressure at 50, 000 feet? 8) 2 marks Determine the indicated value of the following: 10+12+14+....(524) 9) 2 marks Page 4 of 12 10. Determine the sum of the following arithmetic series: 9 + 3 + (-3) +.... + (-123) 10) 2 marks 11. Determine the common difference, d for the arithmetic series given the following values. S11 = 682 and a = 17 11 ) 2 marks 12. Determine n for the arithmetic series given the following values, n is equal for both S,, and t . S = 561, t = 71 and a = 31 12) 2 marks Page 5 of 12l3. Determine the indicated sum for the arithmetic series given the following the values. (1:8, t16=68, 312:? 13) 2 marks 14. When an object is dropped from rest it falls about 5 In in the first second, 15 m in the second, second, 25 m in the third second, and so on. If a rock is dropped from a hot air balloon and takes 16 seconds to hit the ground, how high above the ground is the balloon? l4) 2 marks 15. Determine the sum of all the multiples of 4 between 1 and 999. 15) 2 marks Page 6 of 12 All answers rounded to 2 decimal places unless otherwise stated. 17. Given the geometric sequence 16, 8, 4, a) detennine the general term tn. a) 2 marks b) determine the 13",1 term. b) 2 marks 18. Given the geometric sequence 16, 32, 64, ...., 16 384 a) determine the number of terms in the sequence. a) 2 marks Page 7 of 12 b) which term in the sequence is 2048. b) 2 nmrks 19. Given a geometric sequence with (5 = 162 and t8 = 4374, determine the first 3 terms of the sequence. 19. 2 marks 20. The first three terms of a geometric sequence are x, x + 5 and x + 9. Determine the numerical value of the first three terms. 20. 2 marks Page 8 of 12 21. If the sum of the first 9 terms of a geometric series is 98 410 and the common ratio is 3, determine the value of the first term. 21. 3 nmrks 22. Find the common ratio for each of the following geometric series. Determine whether a sum to infinity exists. Find the sum where it exists. a) 9 + 3 + 1.... r = 1 mark 5 = 2 marks 1 b) 7 1 + ..... 7 r : 1 mark S = 2 marks Page 9 of 12