Sara is training to run a marathon. The first week she runs 5 km each day. The next week, she runs 7 km each day. During each successive week, each day she runs 2 km farther than she ran the days of the previous week. If she runs for five days each week, what total distance will Sara run in a 10 week training session? X B SS ! U S Xz x2 I G C > Thinking and Inquiry - 6 Marks A cereal company attempts to promote its product by placing certificates for a cash prize in selected boxes. The company wants to come up with a number of prizes that satisfy all of these conditions: a) The total of the prizes is at most $2 000 000. b) Each prize is in whole dollars (no cents). c) When the prizes are arranged from least to greatest, each prize is a constant integral multiple of the next smaller prize and is . more than double the next smaller prize . less than 10 times the next smaller prize Determine a set of prizes that satisfies these conditions.Joan is helping a friend understand the formulas for an arithmetic series. She uses linking cubes to represent the sum of the series 2+5+8+11+14 two ways. These representations are shown below. Explain how the linking-cube representations can be used to explain the formulas for an arithmetic series. X > Communication - 2 Marks Describe several methods for calculating the partial sums of an arithmetic and a geometric series. How are the methods similar? different?At a fish hatchery, fish hatch at different times even though the eggs were all fertilized at the same time. The number of fish that hatched on each of the first four days after fertilization was 2, 10, 50, and 250, respectively. If the pattern continues, calculate the total number of fish hatched during the first 10 days. X A . B I U S x2 E I G C Application - 4 Marks Your grandparents put aside $100 for you on your first birthday. Every following year, they put away $75 more than they did the previous year. How much money will have been put aside by the time you are 21?7 971 615 + 5 314 410 + 3 542 940 + ... + 92 160 Calculate the sum of the geometric series above. A . B I E U S Xz x2 E G C Knowledge and Understanding - 3 Marks The 1st, 5th, and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence