Maths Worksheet - Series & Sequences

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 10th March 2009 Number patterns – Series/sequences - Arithmetic 1. Write down the first four terms and the 10th term of the sequence with the general term: a) Tk = k + 4 b) Tk = (-1/3)k c) Tk = (-2)k d) T1 = 5 and Tk + 1 = Tk – 2 for k ≥ 1 e) T1 = 1 and Tk + 1 = 3Tk for k ≥ 1 2. Determine the 10th and 21st terms of each of the following arithmetic sequences: a) 7; 10; 13; … b) 2; -1/2; -3; … c) 4 + 7x; 5 + 9x; 6 + 11x; … d) a = 2/3; d = 1/3 3. Determine which term of the arithmetic sequence: a) 3; 5; 7; … is equal to 27 b) -4; 1; 6; … is equal to 56 c) 13; 10; 7; … is equal to -44 d) 3; 3,5; 4; … is equal to 15,5 4. Determine the first three terms of the arithmetic progression of which: a) the 10th term is 31 and the 15th term is 46 b) the 7th term is 3 and the 12th term is -3 c) the 5th term is 7 + 9x and d = 2x d) the 4th term is -13 and the 7th term is -25 5. If p and q are the fourth and seventh terms respectively of an arithmetic series, determine in terms of p and q a) the common difference b) the sum to ten terms of the series 6. The fifteenth term of ath arithmetic progression a; 3a; … is a2. Calculate the value of a 7. The sum of the first three terms of an AP is 39 and their product is 2 184 a) show that the second term is 13 b) calculate the fourth term of the sequence

∑( − 1 3 ) ∞

8. What is

r

equal to?

r =0

9. What is the sum to infinity of -2; 1; -1/2; …? 10. Expand each of the following: 5

a)

∑k k =1

2

6

b)

k

∑k + 2 k =1

11. Write the following in sigma notation: a) 1 + 2 + 3 + 4 + 5 + 6 c) 1 + 1/2 + 1/3 + 1/4 + 1/5 + … + 1/10

5

c)

∑2

r

r =2

b) 1 + 4 + 9 + 16 + 25 + 36 + 49 d) 1/2 + 2/3 + 3/4 + 4/5 + 5/6 + … + 20/21