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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: 312 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: 15 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: 274 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: 1785 Question a) In a geometric progression, the sum to infinity is equal to eight times the first term. Find the common ratio. b) In an arithmetic progression, the fifth term is 197 and the sum of the first ten terms is 2040. Find the common difference. Solution a) From the given information, we can […]
Hits: 1230 Question a) An athlete runs the first mile of a marathon in 5 minutes. His speed reduces in such a way that each mile takes 12 seconds longer than the preceding mile. i. Given that the nth mile takes 9 minutes, find the value of n. ii. […]
Hits: 3057 Question a) In an arithmetic progression the sum of the first ten terms is 400 and the sum of the next ten terms is 1000. Find the common difference and the first term. b) A geometric progression has first term , common ratio and sum to infinity 6. A second geometric progression has first term , […]
Hits: 1175 Question a) In an arithmetic progression, the sum, , of the first terms is given by . Find the first term and the common difference of the progression. b) The first 2 terms of a geometric progression are 64 and 48 respectively. The first 3 terms of the geometric progression are also the 1st term, […]
Hits: 2010 Question a) The first and last terms of an arithmetic progression are 12 and 48 respectively. The sum of the first four terms is 57. Find the number of terms in the progression. b) The third term of a geometric progression is four times the first term. The sum of the first six terms is k […]
Hits: 691 Question The third term of a geometric progression is −108 and the sixth term is 32. Find i. the common ratio, ii. the first term, iii. the sum to infinity. Solution From the given information, we can compile following data about Geometric Progression (G.P); i. Expression for the general term in […]