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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. wi B. C. D. A/ W 19.3. In a geometric sequence t, = 9000 and to = 15 552. Find the first term. 3. 3 marks 4. Evaluate and show formula used. 64 3) )* - 1 4. 3 marksPART 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? 3 marks b) Write a general term for this arithmetic sequence. 13) 2 marks 2. The sum of the rst three terms in an arithmetic series is 6 and the product of these terms is 24. Find the first three terms. 3 marks 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)6 100 1.1)6 B- ( c. 100(0.9)5 D. 1000.1)5 2]. 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 ten-fold 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. 25 119 times D. 2.6 times 23. 24. 25. 26. 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. 410 times B. 10 000 times C. 4 000 times D. 40 times 24. 8 Determine the first term in the expansion of 2 3(2" ). k=2 A. 3 B. 6 C. 12 D. 36 25. Determine the sum of the innite geometric series: 2 200(0.6)'k_l . k=l A. 125 B. 333 C. 500 D. no finite sum 26