14. For each of the sequences given below1) Write out the first 4 terms of the sequence.2)State whether the sequence is arithmetic or geometric. If the sequence is arithmetic state thecommon difference and if the sequence is geometric state the common ratio.a){a}={10b) {n} = {5+7n}n-1

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Answered: 14. For each of the sequences given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2) A sequence is defined using a recursive definition as: a = 5, a, = 11, and a, = a,-1+ 2a,-2 Determine the value of a,. Show how you found your answer.
2. Write the first five terms of each sequence. Determine whether each sequence is arith geometric, or neither. Note: a(1) = 7 means that the first term of the sequence is 7. a. a(1) = 7,a(n) = a(n – 1) – 3 for n22. This sequence is The first five terms are 7, , and b. b(1) = 2,b(n) = 2-b(n - 1) – 1 for nz2. This sequence is The first five terms are and c. c(1) = 3,c(n) = 10-c(n – 1) for n22. This sequence is The first five terms are and d. d(1) = 1,d(n) = n· d(n – 1) for n22. This sequence is The first five terms are and 1 D00 F4 F5 F10 % & * 5 6 7 8 9
Given two terms in an arithmetic sequence find the common difference. 7) a,-35 and a-83 "36 A) None of these B) d--2 C) d-2 E) d-4 D) d--4
B) How many terms must be taken from the sequence (-16, 14, 12, ...) starting from the first term so that their sum is zero?
10. How many terms are in the sequence 3, 6, 12, 24, 48, ..., 1536? а. 7 b. 8 с. 9 d. 10 11
2. a) Determine an algebraic expression for the nth term of the sequence 7, 10, 13, 16, .... b) Determine an algebraic expression for the nth term of the sequence 8, 11, 14, 17, .... c) Compare your algebraic expressions in parts (a) and (b). (4.2)
Please help me with these two questions
1.) Show that the sequence 2,11, 20, 29, ... is arithmetic.
Using the procedure indicated in the hint, solve each ofthe following Babylonian problems: (a) x = 30, xy − (x − y)2 = 500. [Hint: Subtractthe second equation from the square of the first toget a quadratic in x − y. Solving this quadraticleads to a system of the form x − y = a,xy = b.]

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14. For each of the sequences given below 1) Write out the first 4 terms of the sequence. 2)State whether the sequence is arithmetic or geometric. If the sequence is arithmetic state the common difference and if the sequence is geometric state the common ratio. a) (---) b) (a) = (5+7n)