series and sequences assignment 6

series and sequences assignment 6 - Assignment 6, Sequences...

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Unformatted text preview: Assignment 6, Sequences Due: 26 th November Name: __________________ 1. The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a , and the common difference, d , of the sequence. Working: Answer: .. (Total 4 marks) 2. The ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is 13 6 . If each term of this sequence is positive, and the product of the first term and the third term is 32, find the sum of the first 100 terms of this sequence. (Total 7 marks) Hence, d = 2 and a = 4 and sum to 100 terms of this sequence is 2 100 {(2)(4) + (100 l)2}. (M1) = 10 300 (A1) [7] 1 3. An arithmetic sequence has 5 and 13 as its first two terms respectively. (a) Write down, in terms of n , an expression for the n th term, a n . (b) Find the number of terms of the sequence which are less than 400. Working: Answers : (a) .................................................................. (b) .................................................................. (Total 4 marks) 4. The sum of the first n terms of an arithmetic sequence is S n = 3 n 2 2 n. Find the n th term u n . Working: Answer: .................................................................. (Total 3 marks) 2 5. The probability distribution of a discrete random variable X is given by P ( X = x ) = k x 3 2 , for x = 0, 1, 2, ...... Find the value of k. Working: Answer: .................................................................. (Total 3 marks) 6. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, .... Working: Answer: .................................................................. (Total 3 marks) 3 7. The sum of an infinite geometric sequence is 2 1 13 , and the sum of the first three terms is 13. Find the first term. Working: Answer: .................................................................. (Total 3 marks) 8. Find the sum to infinity of the geometric series .... 3 16 8 12 + + Working: Answer: .. (Total 3 marks) 4 9. The n th term, u n , of a geometric sequence is given by u n = 3(4) n +1 , n + . (a) Find the common ratio r . (b) Hence, or otherwise, find S n , the sum of the first n terms of this sequence. Working: Answers : (a) .................................................................. (b) .................................................................. (Total 3 marks) 10. Consider the infinite geometric series ..... 3 2 3 2 3 2 1 3 2 + + + + x x x (a) For what values of x does the series converge?...
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This note was uploaded on 09/19/2010 for the course MATH 1004 taught by Professor Wilson during the Spring '10 term at International Institute of Information Technology.

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series and sequences assignment 6 - Assignment 6, Sequences...

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