College Algebra 1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: Jay Abramson
1 Prerequisites 2 Equations And Inequalities 3 Functions 4 Linear Functions 5 Polynomial And Rational Functions 6 Exponential And Logarithmic Functions 7 Systems Of Equations And Inequalities 8 Analytic Geometry 9 Sequences, Probability And Counting Theory Chapter9: Sequences, Probability And Counting Theory
9.1 Sequences And Their Notations 9.2 Arithmetic Sequences 9.3 Geometric Sequences 9.4 Series And Their Notations 9.5 Counting Principles 9.6 Binomial Theorem 9.7 Probability Chapter Questions Section9.1: Sequences And Their Notations
Problem 1TI: Write the first five terms of the sequence defined by the explicit formula tn=5n4 . Problem 2TI: Write the first five terms of the sequence. an=4n(2)n Problem 3TI: Write the first six terms of the sequence. an={5n2ifniseven2n3ifnisodd Problem 4TI: Write an explicit formula for the nth term of the sequence. 9,81,729,6,561,59,049,... Problem 5TI: Write an explicit formula for the nth term of the sequence. {34,98,2712,8116,24320,...} Problem 6TI: Write an explicit formula for the nth term of the sequence. {1e2,1e,1,e,e2,...} Problem 7TI: Write the first five terms of the sequence defined by the recursive formula. a1=2an=2an1+1 for n2 Problem 8TI: Write the first 8 terms of the sequence defined by the recursive formula.... Problem 9TI: Write the first five terms of the sequence defined by the explicit formula an=(n+1)!2n Problem 1SE: Discuss the meaning of a sequence. If a finite sequence is defined by a formula, what is its domain?... Problem 2SE: Describe three ways that a sequence can be defined. Problem 3SE: Is the ordered set of even numbers an infinite sequence? What about the ordered set of odd numbers?... Problem 4SE: What happens to the terms an of a sequence when there is a negative factor in the formula that is... Problem 5SE: What is a factorial, and how is it denoted? Use an example to illustrate how factorial notation can... Problem 6SE: For the following exercises, write the first four terms of the sequence. 6. an=2n2 Problem 7SE: For the following exercises, write the first four terms of the sequence. an=16n+1 Problem 8SE: For the following exercises, write the first four terms of the sequence. 8. an=(5)n1 Problem 9SE: For the following exercises, write the first four terms of the sequence. 9. an=2nn3 Problem 10SE: For the following exercises, write the first four terms of the sequence. an=2n+1n3 Problem 11SE: For the following exercises, write the first four terms of the sequence. 11. an=1.25(4)n1 Problem 12SE: For the following exercises, write the first four terms of the sequence. 12. an=4(6)n1 Problem 13SE: For the following exercises, write the first four terms of the sequence. an=n22n+1 Problem 14SE: For the following exercises, write the first four terms of the sequence. a n = ( 10 ) n +1 Problem 15SE: For the following exercises, write the first four terms of the sequence. 15. an=(4(5)n15) Problem 16SE: For the following exercises, write the first four terms of the sequence. 16.... Problem 17SE: For the following exercises, write the first four terms of the sequence. 17. an={n25ifn5n22n+1ifn5 Problem 18SE: For the following exercises, write the first four terms of the sequence. 18.... Problem 19SE: For the following exercises, write the first eight terms of the piecewise sequence. 19.... Problem 20SE: For the following exercises, write the first eight terms of the piecewise sequence. 20.... Problem 21SE: For the following exercises, write an explicit formula for each sequence. 21. 4,7,12,19,28,... Problem 22SE: For the following exercises, write a recursive formula for each sequence. 22. 4,2,10,14,34 Problem 23SE: For the following exercises, write an explicit formula for each sequence. 23. 1,1,43,2,165,... Problem 24SE: For the following exercises, write an explicit formula for each sequence. 24.... Problem 25SE: For the following exercises, write an explicit formula for each sequence. 112,14,18,116,.... Problem 26SE: For the following exercises, write a recursive formula for each sequence. a1=9,an=an1+n Problem 27SE: For the following exercises, write the first five terms of the sequence. a1=3,an=(3)an1 Problem 28SE: For the following exercises, write the first five terms of the sequence. a1=4,an=an1+2nan11 Problem 29SE: For the following exercises, write the first five terms of the sequence. 29. a1=1,an=(3)n1an12 Problem 30SE: For the following exercises, write the first five terms of the sequence. 30. a1=30,an=(2+an1)(12)n Problem 31SE: For the following exercises, write the first eight terms of the sequence. 31.... Problem 32SE: For the following exercises, write the first eight terms of the sequence. an=1,an=5,an=an2(3an1) Problem 33SE: For the following exercises, write the first eight terms of the sequence. 33.... Problem 34SE: For the following exercises, write a recursive formula for each sequence. 34. 2.5,5,10,20,40,... ... Problem 35SE: For the following exercises, write a recursive formula for each sequence. 35. 8,6,3,1,6,... Problem 36SE: For the following exercises, write a recursive formula for each sequence. 36. 2,4,12,48,240,... Problem 37SE: For the following exercises, write a recursive formula for each sequence. 37. 35,38,41,44,47,... Problem 38SE: For the following exercises, write a recursive formula for each sequence. 38. 15,3,35,325,3125,.... Problem 39SE: For the following exercises, evaluate the factorial. 39. 6! Problem 40SE: For the following exercises, evaluate the factorial. 40. (126)! Problem 41SE: For the following exercises, evaluate the factorial. 41. 12!6! Problem 42SE: For the following exercises, evaluate the factorial. 42. 100!99! Problem 43SE: For the following exercises, write the first four terms of the sequence. 43. an=n!n2 Problem 44SE: For the following exercises, write the first four terms of the sequence. 44. an=3n!4n! Problem 45SE: For the following exercises, write the first four terms of the sequence. 45. an=n!n2n1 Problem 46SE: For the following exercises, write the first four terms of the sequence. 46. an=100nn(n1)! Problem 47SE: For the following exercises, graph the first five terms of the indicated sequence 47. an=(1)nn+n Problem 48SE: For the following exercises, graph the first five terms of the indicated sequence 48.... Problem 49SE: For the following exercises, graph the first five terms of the indicated sequence 49.... Problem 50SE: For the following exercises, graph the first five terms of the indicated sequence 50. an=1,an=an1+8 Problem 51SE: For the following exercises, graph the first five terms of the indicated sequence 51. an=(n+1)!(n1) Problem 52SE: For the following exercises,write an explicit formula for the sequence using the first five points... Problem 53SE: For the following exercises, write an explicit formula for the sequence using the first five points... Problem 54SE: For the following exercises, write an explicit formula for the sequence using the first five points... Problem 55SE: For the following exercises, write a recursive formula for the sequence using the first five points... Problem 56SE: For the following exercises, write a recursive formula for the sequence using the first five points... Problem 57SE: Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the... Problem 58SE: Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the... Problem 59SE: Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the... Problem 60SE: Follow these steps to evaluate a sequence defined recursively using a graphing calculator: •On the... Problem 61SE: Follow these steps to evaluate a sequence defined recursively using a graphing calculator: • On the... Problem 62SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do... Problem 63SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do... Problem 64SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do... Problem 65SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do... Problem 66SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do... Problem 67SE: Consider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result. Problem 68SE: What term in the sequence an=n2+4n+42(n+2) has the value 41? Verify the result. Problem 69SE: Find a recursive formula for the sequence 1,0,1,1,0,1,1,0,1,1,0,1,1,... (Hint: find a pattern for an... Problem 70SE: Calculate the first eight terms of the sequences an=(n+2)!(n1)! and bn=n3+3n32n , and then make a... Problem 71SE: Prove the conjecture made in the preceding exercise. Problem 71SE: Prove the conjecture made in the preceding exercise.
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Where C is complex numbers and R is real numbers.
Transcribed Image Text: (d) Check whether or not [C: R] is an
algebraic extension.
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
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![(d) Check whether or not [C: R] is an
algebraic extension.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8631c735-46d2-42de-a91f-1aa2ee947e73%2F4e0a0e44-ab74-45e3-bf03-8afb108bc786%2Fckuk5avb_processed.jpeg&w=3840&q=75)
