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Hits: 48 Question The first three terms of an arithmetic progression are 4, x and y respectively. The first three terms of a geometric progression are x, y and 18 respectively. It is given that both x and y are positive. a) Find the value of x and the value of y. b) Find the […]
Hits: 106 Question The first term of a series is 6 and the second term is 2. i. For the case where the series is an arithmetic progression, find the sum of the first 80 terms. ii. For the case where the series is a geometric progression, find the sum to infinity. Solution […]
Hits: 822 Question On a certain day, the height of a young bamboo plant was found to be 40 cm. After exactly one day its height was found to be 41.2 cm. Two different models are used to predict its height exactly 60 days after it was first measured. · Model A assumes that the […]
Hits: 215 Question The common ratio of a geometric progression is 0.99. Express the sum of the first 100 terms as a percentage of the sum to infinity, giving your answer correct to 2 significant figures. Solution We are given that common ration of a Geometric Progression is; Expression for Common Ratio () in a […]
Hits: 556 Question A company producing salt from sea water changed to a new process. The amount of salt obtained each week increased by 2% of the amount obtained in the preceding week. It is given that in the first week after the change the company obtained 8000 kg of salt. i. Find the amount […]
Hits: 726 Question a) A geometric progression has a second term of 12 and a sum to infinity of 54. Find the possible values of the first term of the progression. b) The nth term of a progression is p + qn, where p and q are constants, and Sn is the sum of the […]
Hits: 455 Question A company, which is making 140 bicycles each week, plans to increase its production. The number of bicycles produced is to be increased by d each week, starting from 140 in week 1, to 140 + d in week 2, to 140 + 2d in week 3 and so on, until the company is producing 206 […]
Hits: 74 Question A sequence is defined by , , Where k is a positive constant. a) Write down expressions for and in terms of k, giving your answers in their simplest form. Given that , b) Find an exact value for k. Solution a. We are given that sequence is defined by We are required to find […]
Hits: 210 Question On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This first gift was £60 and on each subsequent birthday the gift was £15 more than the year before. The amounts of these gifts form an arithmetic sequence. a. Show that, immediately after his 12th birthday, the […]
Hits: 34 Question A sequence is defined by , Where is a constant. a) Write down expressions for and in terms of k. Find, b) in terms of k, giving your answer in its simplest form. c) . Solution a) We are given that sequence is defined by We are required to find and . We can utilize the […]
Hits: 164 Question Jess started work 20 years ago. In year 1 her annual salary was £17000. Her annual salary increased by £1500 each year, so that her annual salary in year 2 was £18500, in year 3 it was £20000 and so on, forming an arithmetic sequence. This continued until she reached her maximum annual salary […]
Hits: 37 Question i. A sequence is defined by , and Find the value of a) b) ii. A sequence is defined by , and , where k is a constant a) Find and in terms of k. Given that , b) Find the value of k. Solution i. a) We are given that sequence is […]
Hits: 486 Question Xin has been given a 14 day training schedule by her coach. Xin will run for A minutes on day 1, where A is a constant. She will then increase her running time by (d + 1) minutes each day, where d is a constant. a. Show that on day 14, Xin will run […]
Hits: 27 Question A sequence is defined by , for Where is a constant. a) Find an expression for in terms of k. Given that , b) Find the value of k. Solution a) We are given that sequence is defined by We are required to find . We can utilize the given expression for general terms beyond […]
Hits: 78 Question In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the year before, so that the shop sold 160 computers in 2001, 170 computers in 2002, and so on forming an arithmetic sequence. a. Show that the shop sold 220 computers in 2007. b. Calculate the total […]
Hits: 31 Question A sequence of numbers is defined by , for Given that , .a) Find the value of . b) Find the value . Solution a. We are given that sequence is defined by We are required to find when . We can utilize the given expression for general terms beyond first term as; We are given that […]
Hits: 249 Question Shelim starts his new job on a salary of £14 000. He will receive a rise of £1500 a year for each full year that he works, so that he will have a salary of £15 500 in year 2, a salary of £17 000 in year 3 and so on. When Shelim’s salary reaches […]
Hits: 32 Question Given that for all positive integers n, a) find the value of b) Find the value of Solution a. We are given that; We are required to find . Therefore, we substitute n=5; b. We are required to find . We can find as follows; Therefore ;
Hits: 25 Question Each year, Abbie pays into a saving scheme. In the first year she pays in £500. Her payments the increase by £200 each year so that she pays £700 in the second year, £900 in the third year and so on. a. Find out how much Abbie pays into the saving scheme in the […]
Hits: 14 Question A sequence is defined by , Where is a constant, . a) Write down an expression for in terms of k. b) Show that Given also that c) Calculate the value of k. d) Hence, find the value of . Solution a. We are given that sequence is defined by We are […]