Write down the common difference. (1) Find the number of terms in the sequence. (3) Find the sum of the sequence. (2) (Total 6 marks)

Transcription

1 Arithmetic Sequence and Series 1. Consider the arithmetic sequence 3, 9, 15,..., Write down the common difference. (1) Find the number of terms in the sequence. (c) Find the sum of the sequence. 2. In an arithmetic sequence, u 1 = 2 and u 3 = 8. Find d. Find u 20. (c) Find S In an arithmetic sequence u 21 = 37 and u 4 = 3. Find (i) the common difference; the first term. Find S 10. (Total 7 marks) IB Questionbank Maths SL 1

2 4. Consider the arithmetic sequence 2, 5, 8, 11,... Find u 101. Find the value of n so that u n = In an arithmetic sequence, the first term is 5 and the fourth term is 40. Find the second term. 6. In an arithmetic sequence u 1 = 7, u 20 = 64 and u n = Find the value of the common difference. Find the value of n. (Total 5 marks) 7. An arithmetic sequence, u 1, u 2, u 3,..., has d = 11 and u 27 = 263. Find u 1. (i) Given that u n = 516, find the value of n. For this value of n, find S n. IB Questionbank Maths SL 2

3 8. The first three terms of an arithmetic sequence are 7, 9.5, 12. What is the 41 st term of the sequence? What is the sum of the first 101 terms of the sequence? 9. The n th term of an arithmetic sequence is given by u n = 5 + 2n. Write down the common difference. (1) (i) Given that the n th term of this sequence is 115, find the value of n. For this value of n, find the sum of the sequence. (5) 10. Find the sum of the arithmetic series In an arithmetic sequence, S 40 = 1900 and u 40 = 106. Find the value of u 1 and of d. 12. In an arithmetic series, the first term is 7 and the sum of the first 20 terms is 620. Find the common difference. Find the value of the 78 th term. (Total 5 marks) IB Questionbank Maths SL 3

4 13. In an arithmetic sequence, the first term is 2, the fourth term is 16, and the n th term is Find the common difference d. Find the value of n. 14. Let S n be the sum of the first n terms of an arithmetic sequence, whose first three terms are u 1, u 2 and u 3. It is known that S 1 = 7, and S 2 = 18. Write down u 1. Calculate the common difference of the sequence. (c) Calculate u Let u n = 3 2n. Write down the value of u 1, u 2, and u Find (3 2n ). n= Write down the first three terms of the sequence u n = 3n, for n 1. (1) Find (i) 20 n= n= 21 3n ; 3n. (5) IB Questionbank Maths SL 4

5 17. Let S n be the sum of the first n terms of the arithmetic series Find (i) S 4 ; S 100. Let M = (i) Find M 2. Show that M =. 0 1 (5) It may now be assumed that M n = 1 2n, for n 4. The sum Tn is defined by 0 1 (c) (i) Write down M 4. T n = M 1 + M 2 + M M n. Find T 4. (d) Using your results from part, find T 100. (Total 16 marks) 18. An arithmetic series has five terms. The first term is 2 and the last term is 32. Find the sum of the series. IB Questionbank Maths SL 5

6 19. A theatre has 20 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of seats has two more seats in it than the previous row. Calculate the number of seats in the 20th row. Calculate the total number of seats. 20. Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans shown has 5 cans in the bottom row and 4 cans in the row above it. A pile has 20 cans in the bottom row. Show that the pile contains 210 cans. There are 3240 cans in a pile. How many cans are in the bottom row? (c) (i) There are S cans and they are organized in a triangular pile with n cans in the bottom row. Show that n 2 + n 2S = 0. Clara has 2100 cans. Explain why she cannot organize them in a triangular pile. (6) (Total 14 marks) IB Questionbank Maths SL 6

7 21. Arturo goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for one year (52 weeks). How far does Arturo swim in the final week? How far does he swim altogether? 22. Each day a runner trains for a 10 km race. On the first day she runs 1000 m, and then increases the distance by 250 m on each subsequent day. On which day does she run a distance of 10 km in training? What is the total distance she will have run in training by the end of that day? Give your answer exactly. IB Questionbank Maths SL 7