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Hits: 818 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: 85 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: 316 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: 42 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: 326 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: 39 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: 646 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: 29 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: 113 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: 32 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: 401 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: 33 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: 31 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: 17 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 […]
Hits: 379 Question A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produced is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N. […]
Hits: 17 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 two possible values 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 […]
Hits: 295 Question Lewis played a game of space invaders. He scored points for each spaceship that he captured. Lewis scored 140 points for capturing his first spaceship. He scored 160 points for capturing his second spaceship, 180 points for capturing his third spaceship, and so on. The number of points scored for capturing each successive spaceship formed an arithmetic […]
Hits: 11 Question A sequence satisfies , , Given that , a) Find the value of and the value of . b) Evaluate . Solution a) We are given that sequence is defined by We are given that and required to find . We can utilize the given expression for general terms beyond first term as; Similarly, we can find […]
Hits: 76 Question A boy saves some money over a period of 60 weeks. He saves 10p in week 1, 15p in week 2, 20p in week 3 and so on until week 60. His weekly savings form an arithmetic sequence. a. Find how much he saves in week 15 b. Calculate the total amount he […]
Hits: 14 Question A sequence of numbers is defined by , Where is a constant. a) Write down an expression, in terms of c, for . b) Show that Given that c) Find a range of values of c. Solution a) We are given that sequence is defined by We are required to find . We […]