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. format_list_bulleted
![The image shows a mathematical expression related to products in sequences:
\[
\prod_{k=1}^{n} a_{k}, \text{ for } n \geq 1
\]
This expression represents the product of a sequence of terms \( a_k \), starting from \( k = 1 \) up to \( k = n \). The condition \( n \geq 1 \) indicates that the product is defined only for positive integer values of \( n \). Therefore, it calculates the multiplication of the terms \( a_1 \times a_2 \times \cdots \times a_n \). This notation is often used in mathematics to succinctly represent such multiplicative processes in sequences.](https://content.bartleby.com/qna-images/question/bfcb3af0-6e5c-49af-8aa4-5de9c395dfb0/ee67df0d-ecac-499e-8874-9236df574a9a/1iex21b_processed.jpeg)
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