Solve the following problems. Write your complete solutions on a separate sheet of paper 1. A man repays a loan of 65,000 by paying 400 in the first month and then increasing the payment by 300 every month. How long will it take for him to clear the loan? 2. A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two bricks less than the previous step. a How many bricks are required for the top most step? b. How many bricks are required to build the stair case? 3. In the year 2000, a shop sold 150 computers. Each year the shop sold 10 more computers than the year before, so the shop sold 160 computers in 2001, 170 computers in 2002, and so on. a. Show that the shop sold 220 computers in 2007. b. Calculate the total number of computers the shop sold from 2000 to 2013 inclusive, 4. Riley played an adventure game. He scored points for each dragon that he captured. The number of points that Riley scored for capturing each successive dragon formed an arithmetic sequence. Riley captured n dragons and the total number of points that he scored for capturing all n dragons was 8500. Given that Riley scored 300 points for capturing his first dragon and then 700 points for capturing her nth dragon, find the value of n 5. A 40-year building program for new houses began in the year 1951 (Year 1) and finished in 1990 (Year 40). The number of houses built each year form an arithmetic sequence with first term a, and common difference d. Given that 2400 new houses were built in 1960 and 600 new houses were built in 1990, find a. the value of d. b. the value of a. c. the total number of houses built over the 40-year period. 2