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MCR3UW **NO GDC** 1. Consider the arithmetic sequence 3, 7, 11, 15, … a) Write down the common difference. b) Date: ________________________ Find ๐ข71 c) Find the value of ๐ such that ๐ข๐ = 99 2. The first three terms of an infinite geometric sequence are 64, 16, and 4. a) Write down the value of ๐. b) Find ๐ข4 . c) Find the sum to infinity of this sequence. 3. In an arithmetic sequence ๐ข6 = 25 and ๐ข12 = 49 a) Find the common difference b) Find the first term of the sequence. 4. Consider the arithmetic sequence 22, ๐ฅ, 38, … a) Find the value of ๐ฅ. b) Find ๐ข31 5. Evaluate the expression ∑4๐=1(3๐ ). 6. Consider the geometric series 800 + 200 + 50 + โฏ a) Find the common ratio. b) Find the sum to infinity. 7. Find all possible values of ๐ฅ such that this sequence is geometric: ๐ฅ, 12, 9๐ฅ, … 8. A grocery store has a display of soup cans stacked in a pyramid. The top row has three cans, and each row has two more cans than the row above it. a) If there are 35 cans in the bottom row, how many are in the display? b) How many cans in the display in total? **WIT GDC** 9. In an arithmetic series, the first term is 4 and the sum of the first 25 terms is 1000. a) Find the common difference. b) Find the value of the 17th term. 10. Consider the arithmetic sequence 3, 4.5, 6, 7.5, … a) Find ๐ข63 b) Find the value of ๐ such that ๐๐ = 840 11. In an arithmetic series, the tenth term is 25 and the sum of the first 10 terms is 160. a) Find the first term and the common difference. b) Find the sum of the first 24 terms. 12. In a geometric sequence, the first term is 3 and the sixth term is 96. a) Find the common ratio. b) Find the least value of ๐ such that ๐ข๐ > 3000. 13. In an arithmetic sequence, the first term is 28 and the common difference is 50. In a geometric sequence, the first term is 1 and the common ratio is 1.5. Find the least value of ๐ such that the ๐๐กโ term of the geometric sequence is greater than the ๐๐กโ term of the arithmetic sequence. 14. In a geometric series, the 3rd term is 45 and the sum of the first 7 terms is 2735. Find the first term and the common ratio, ๐, if ๐ ∈ โค. 15. At the beginning of 2010, the population of a country was 3.4 million. a) If the population grows at a rate of 1.6% annually, estimate the country’s population at the beginning of 2040. b) If the population growth continues at this rate, in what year would the population of the country be expected to exceed 7 million? 7) ±4 8a) 17 8b) 323 9a) 3 9b) 52 10a) 96 2b) 32 11a) ๐ข1 = 7, ๐ = 2 11b) 720 4a) 2 4b) 11 13) 18 14) ๐ข1 = 5, ๐ = −3 15a) ≈ 5.47 million 15b) 2056 6a) 4 1 6b) 3 3200 3a) 4 3b) 5 4a) 30 4b) 5 5) 120 2a) 4 1 2b) 1 Answers 1a) 4 1b) 283 **These questions are from Mathematics Standard Level, published by Oxford** 2c) 3 256 1c) 25