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Algebra 1 cc Function 4 Evaluate and write arithmetic sequences

Algebra 1 cc Function 4 Evaluate and write arithmetic sequences. Recall: A function is relation in which each element of the domain is paired with exactly one element of the range. A sequence is a function whose domain is the set of natural numbers. Domain = {1,2,3,4,…}. Example

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Algebra 1 cc Function 4 Evaluate and write arithmetic sequences

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  1. Algebra 1 cc Function 4Evaluate and write arithmetic sequences Recall: A function is relation in which each element of the domain is paired with exactly one element of the range. A sequence is a function whose domain is the set of natural numbers. Domain = {1,2,3,4,…} Example tn = 2n + 5 t1 = 2(1) + 5 = 7 t2= 2(2) + 5 = 9 t3= 2(3) + 5 = 11 t4= 2(4) + 5 = 13 The 1st four terms of the sequence are {7,9,11,13} A special notation is used for sequences.. Sequence Notation t1 = 1st term of the sequence t2 = 2nd term of the sequence t3 = 3rd term of the sequence tn = nth term of the sequence

  2. Find the 1st five terms of the sequence given by the formula: tn = n2 + 5 Find the 1st five terms of the sequence given by the formula: tn = 2n - 5

  3. Which formula expresses the sequence: {5, 9, 15, 23, 33…} • tn= 4n + 1 • tn = 2n2 + 3 • tn = n2 + n + 3

  4. There are many different types of sequences. A sequence is arithmetic if the difference “d” between any two consecutive terms is constant. The sequence: {5,8,11,14,17,20,…} is arithmetic because 8-5=3, 11-8=3, 14-11=3, … d=3

  5. Which of the following are arithmetic sequences? • {5, 11, 17, 23, 29, 35, …} • {5, 10, 20, 40, 80, 160, …} • {60, 55, 50, 45, 40, …} • {1, 4, 9, 16, 25, 36, …}

  6. The general formula for the nth term of an arithmetic sequence is:tn = t1 + (n-1)d, where n is the number of the term and d is the common difference. Give the formula for the nth term of the sequence: {7, 11, 15, 19, 23, ….} Find the 70th term. Give the formula for the nth term of the sequence: {77,66,55,44 ….} Find the 20thterm.

  7. A tree is 7 foot tall when it is transplanted. It grows by 2.5 feet each year. Write a formula for an arithmetic sequence that shows the height of the tree each year. How tall will it be after 6 years?

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