Sequences and Series



The area of the largest equilateral triangle in the diagram, triangle 1, is 4096 cm2. The second triangle is the result of joining the midpoints of the sides of the first triangle. The third and other triangles were also drawn this way.Create a sequence by determining the area of each of the first four triangles.Find the general term of this sequence.What is the area of the eighth triangle?Todd fractured his wrist while he was Rollerblading. To relieve the pain, his doctor suggested that he take 500 mg of aspirin every 6 h. At this rate, only 26% of the aspirin remains in his body by the time he takes a new dose.What quantity of aspirin is in his body after the 3rd dose?Write a recursive formula for this sequence.A researcher is studying fruit flies. Under the laboratory conditions, each generation of fruit flies is 20% more numerous than the preceding generation. a) If the researcher started with 50 fruit flies, estimate the number in the sixth generation. (The original 50 fruit flies is the first generation.)b) Including the sixth generation, how many fruit flies in total could the researcher have studied?A pile of bricks has 85 bricks in the bottom row, 81 bricks in the second row, 77 bricks in the third row, and so on. There is only one brick in the top row.How many bricks are there in the 13th row?How many rows are there in the pile?The half-life of a radioactive substance is 10 min. How much of 500 g of this substance will remain after 8 h?A colony of bacteria doubles in number every 20 min. The initial population of the colony is 20 bacteria. How many bacteria are there after 4 h?A military unit buys 10 spare parts during the first month of a contract, 15 spare parts in the second month, 20 spare parts in the third month, 25 spare parts in the fourth month, and so on. The acquisitions officer wants to know the total number of spare parts the unit will have after 24 months.A hockey arena has 10 920 seats. The first row of seats around the rink has 220 seats. The number of seats in each subsequent row increases by 16.How many rows of seats does the arena have?The arena’s owners would like to expand the arena by adding four more rows of seats. What will be the new capacity of the arena?Amy drops a ball from a height of 16 m. Each time the ball touches the ground, it bounces up to 58 of the maximum height of the previous bounce. Determine the total vertical distance the ball has travelled when it touches the ground for the seventh time. Express your answer to two decimal places.When you shut off a circular saw, it continues to turn for a while. Each second, the speed or revolutions per second, r/s, is 23 of the speed of the previous second. At the beginning of the ninth second, the saw has turned a total of 258 times. What was the speed of the saw at the beginning of the first second when it was first shut off? Express your answer to one decimal place.Answers1. a) 4096, 1024, 256, 64 b) tn=409614n-1c) 142. a) 663.8b) tn = 500 + 0.26tn-13. a) 124b) 4964. a) 37b) 221.776 x 10 – 12 g819201620a) 26b)13 56066.15 m88.3 r/s ................
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