arithmetic sequences & explicit and Recursive formulas unit 1 day 16

A-CED. 4: I can rearrange formulas to highlight a quantity of interest A-CED.4: I can rearrange formulas to highlight a quantity of interest. F-BF.A.2: I can construct linear functions given a description of a relationship or two input-output pairs. F-IF.A.3: I recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of integers.

exploration You have been offered a job paying $28,000 in the first year. You anticipate receiving a $1500 raise each year for the next 7 years. How much will you be earning in the 8th year? How much will you earn over the 8-year period?

How much will you be earning in the 8th year? $28000 +$1500+$1500+$1500+$1500+$1500+$1500+$1500 = $38,500 How much will you earn over the 8-year period? $28000+$29500+$31000+$32500+$34000+$35500+$37000+$38500 = $266,000

ANALYZING your solution think-pair-share activity Describe the pattern you recognized in the solution to both questions. What is the difference between any two consecutive terms in the first and second solution? Describe the difference in the mathematical approach used to find the solution of each question. Can you construct linear function that models the information from the first solution? The functions should allow you to find the nth term of the sequence.

How to define an explicit and recursive formula for an arithmetic sequence Take notes while watching the video. Only watch a portion of this video (0:00 – 4:20) https://www.khanacademy.org/math/precalculus/seq-induction/sequences- review/v/arithmetic-sequences

Identifying arithmetic sequences Decide whether each sequence is arithmetic.

Sage & scribe activity Turn to your partner and explain the reasoning to each answer. Then write a rule for the nth term of the sequence for each “YES” example below. Evaluate the sequence for the 9th term in the sequence.

Guided practice u1a16 Example 1

Guided practice u1a16 Example 2

independent practice u1a16 Example 3 Rewrite the sequence as an explicit and recursive rule. Evaluate the sequence for the given nth term.

independent practice u1a16 Example 3

independent practice u1a16 Example 3

independent practice u1a16 Example 3

independent practice u1a16 Example 3

The first row of a concert hall has 25 seats, and each row after the first has one more seat than the row before it. There are 32 rows of seats. Write the sequence as an explicit rule modeling the number of seats in the nth role. Thirty-five students from a class want to sit in the same row. How close to the front can they sit?

Write the sequence as an explicit rule modeling the number of seats in the nth role. 1st row has 25 seats fixed difference from one row to the next is one additional seat (front to back)

Thirty-five students from a class want to sit in the same row Thirty-five students from a class want to sit in the same row. How close to the front can they sit? The class can sit in the 11th row.

Suppose you buy a $500 camcorder on layaway by making a down payment of $150 and then paying $25 per month. Write a recursive rule for the total amount of money paid on the camcorder at the beginning of the nth month. How much will you have left to pay on the camcorder at the beginning of the twelfth month?

Write a recursive rule for the total amount of money paid on the camcorder at the beginning of the nth month.

How much will you have left to pay on the camcorder at the beginning of the twelfth month? At the beginning of the twelfth month, you would still own $75.