Announcements Short Unit Today – constructing arithmetic sequences Arithmetic sequences WS due Tuesday Monday – modeling with sequences Tuesday – performance task (summative)

What we’re learning today: Given an explicit rule (function) for a sequence, how to find number in the sequence. Given a sequence of numbers, how to find the explicit rule.

A go-kart racing track charges $5 for a go-kart license and $2 for each lap. If you list the charges for 1 lap, 2 laps, 3 laps, and so on, in order, the list forms a sequence of numbers: 7, 9, 11, 13,… Common difference: the difference between two consecutive terms Arithmetic sequence: A sequence that has a common difference

Explicit Rule An explicit rule for a sequence defines the nth term as a function of n for any whole number n greater than 0. Explicit rules can be used to find any specific term in a sequence without finding any of the previous terms. For the previous problem, the explicit rule is: 7, 9, 11, 13,… f(n) = 2n + 5 Use the explicit rule to find the 15th, 16th, and 17th numbers in the sequence

Explore: Write an explicit rule for each sequence: 1. 2. 3. Lucia knows the fourth term in a sequence is 55 and the ninth term in the same sequence is 90. Explain how she can find the common difference for the sequence. Then find the second term of the sequence. Challenge: Write an explicit rule for the following sequence (hint: everything we just learned about how to write explicit rules won’t work here because this isn’t an arithmetic sequence, so you will have to be creative). 1 2 , 2 3 , 3 4 , 4 5 ,…

Write the explicit rule for the sequence 2, 5 2 , 3, 7 2 , ….

Write: How do you write the explicit rule for the sequence 18, 17, 16, …