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Hits: 285 Question i. In the binomial expansion of , the first three terms are . Find the remaining three terms of the expansion. ii. Hence find the coefficient of in the expansion of . Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard form. In the given […]
Hits: 443 Question a.In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five terms. The first term is . i.Show that the common difference of the progression is . ii.Given that the tenth term is 36 more than the fourth term, find the value of […]
Hits: 227 Question Find the coefficient of x in the expansion of . Solution We are required to find the coefficient of in the expansion of given expression. We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the […]
Hits: 123 Question a) The third and fourth terms of a geometric progression are and respectively. Find the sum to infinity of the progression. b) Two schemes are proposed for increasing the amount of household waste that is recycled each week. Scheme A is to increase the amount of waste recycled each month by 0.16 […]
Hits: 216 Question i. The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is greater than 1000p. Show that 2n > 1001. ii. In another case, p and 2p are the first and second terms […]
Hits: 118 Question In an arithmetic progression the first term is and the common difference is 3. The nth term is 94 and the sum of the first terms is 1420. Find and . Solution We can compile following data from the given information for Arithmetic Progression (A.P) ; First we consider the nth term […]
Hits: 301 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: 214 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: 1095 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: 438 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: 921 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: 1308 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: 733 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: 83 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: 298 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: 313 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: 38 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: 627 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 […]