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Hits: 0 Question a. Calculate the sum of all the even numbers from 2 to 100 inclusive, 2 + 4 + 6 + …… + 100 b. In the arithmetic series k + 2k + 3k + …… + 100 k is a positive integer and k is a factor of 100. i. Find, in terms of k, […]
Hits: 0 Question A sequence is defined by , Where is a positive integer. a) Write down an expression for in terms of k. b) Show that c) i. Find in terms of k, I its simplest form. ii. Show that is divisible by 6. Solution a) We are given that sequence is defined by We are […]
Hits: 3 Question An arithmetic sequence has first term a and common difference d. The sum of the first 10 terms of the sequence is 162. a. Show that 10a + 45d =162 Given also that the sixth term of the sequence is 17, b. write down a second equation in a and d, c. find the value of a and […]
Hits: 2 Question A sequence is defined by Where is a constant. a) Find an expression for in terms of c. Given that , b) Find the value of c. 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 first term […]
Hits: 3 Question A farmer has a pay scheme to keep fruit pickers working throughout the 30 day season. He pays £a for their first day, £(a + d ) for their second day, £(a + 2d ) for their third day, and so on, thus increasing the daily payment by £d for each extra day they […]
Hits: 3 Question A sequence of positive numbers is defined by , a) Find and , leaving your answers in surd form. b) Show that . Solution a) We are given that sequence is defined by , We are required to find and . We can utilize the given expression for general terms beyond first term as; […]
Hits: 2 Question Jill gave money to a charity over a 20-year period, from Year 1 to Year 20 inclusive. She gave £150 in Year 1, £160 in Year 2, £170 in Year 3, and so on, so that the amounts of money she gave each year formed an arithmetic sequence. a. Find the amount of money […]
Hits: 7 Question A sequence is defined by , , Where is a constant. a) Write down an expression for in terms of k. b) Show that . Given that , c) Find the value of k. Solution a) We are given that sequence is defined by We are required to find . We can utilize the […]
Hits: 3 Question A 40-year building programme for new houses began in Oldtown in the year 1951 (Year 1) and finished in 1990 (Year 40). The numbers 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 […]
Hits: 11 Question The first term of an arithmetic series is a and the common difference is d. The 18th term of the series is 25 and the 21st term of the series is . a. Use this information to write down two equations for a and d. b. Show that a = –17.5 and find […]
Hits: 7 Question Sue is training for a marathon. Her training includes a run every Saturday starting with a run of 5 km on the first Saturday. Each Saturday she increases the length of her run from the previous Saturday by 2 km. a. Show that on the 4th Saturday of training she runs 11 km. b. […]
Hits: 11 Question A sequence x1, x2, x3, …. ……. is given by: x1=1, xn+1=axn – 3, n≥1, where a is a constant. a. Find an expression for x2 in terms of a. b. Show that x3=a2 – 3a – 3. Given that x3=7, c. find the possible values of a. Solution a. We are given […]
Hits: 10 Question The first term of an arithmetic sequence is 30 and the common difference is –1.5. a. Find the value of the 25th term. The rth term of the sequence is 0. b. Find the value of r. The sum of the first n terms of the sequence is Sn. c. Find the largest positive […]
Hits: 3 Question A sequence is given by: x1=1, xn+1=xn(p+ xn), where p is a constant (p≠0) . a. Find x2 in terms of p. b. Show that x3=1+3p+2p2. Given that x3=1, c. find the value of p, d. (d) write down the value of x2008 . Solution a. We are given the sequence […]
Hits: 3 Question A sequence is defined by , , Where is a positive integer. a) Write down an expression for a in terms of k. b) Show that . c) i. Find in terms of k. ii. Show that is divisible by 10. Solution a) We are […]
Hits: 3 Question A girl saves money over a period of 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence. a. Find the amount she saves in Week 200. b. Calculate her total savings over the […]
Hits: 2 Question Ann has some sticks that are all of the same length. She arranges them in squares and has made the following 3 rows of patterns: She notices that 4 sticks are required to make the single square in the first row, 7 sticks to make 2 squares in the second row and in the […]
Hits: 9 Question An athlete prepares for a race by completing a practice run on each of 11 consecutive days. On each day after the first day, he runs further than he ran on the previous day. The lengths of his 11 practice runs form an arithmetic sequence with first term a km and common difference d km. He […]
Hits: 10 Question A sequence a1, a2, a3, . . . is defined by a1 = 3 an+1 = 3an– 5, n1. a. Find the value of a2 and the value of a3. b. Calculate the value of Solution a. We are given that; an+1 = 3an – 5 a1 = 3 Therefore, we […]
Hits: 13 Question On Alice’s 11th birthday she started to receive an annual allowance. The first annual allowance was £500 and on each following birthday the allowance was increased by £200. a. Show that, immediately after her 12th birthday, the total of the allowances that Alice had received was £1200. b. Find the amount of Alice’s annual allowance […]
