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.

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Presentation transcript:

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 special notation is used for sequences.. Sequence Notation t 1 = 1 st term of the sequence t 2 = 2 nd term of the sequence t 3 = 3 rd term of the sequence t n = n th term of the sequence A sequence is a function whose domain is the set of natural numbers. Domain = {1,2,3,4,…} Example t n = 2n + 5 t 1 = 2(1) + 5 = 7 t 2 = 2(2) + 5 = 9 t 3 = 2(3) + 5 = 11 t 4 = 2(4) + 5 = 13 The 1 st four terms of the sequence are {7,9,11,13}

Find the 1 st five terms of the sequence given by the formula: t n = n Find the 1 st five terms of the sequence given by the formula: t n = 2 n - 5

Which formula expresses the sequence: {5, 9, 15, 23, 33…} a.t n = 4n + 1 b.t n = 2n c.t n = n 2 + n + 3

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

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

The general formula for the nth term of an arithmetic sequence is: t n = t 1 + (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 70 th term. Give the formula for the nth term of the sequence: {77,66,55,44 ….} Find the 20 th term.

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?