Module 3: Linear and Exponential Functions

Lesson 2: Recursive Formulas for Sequences

You will be able to – write recursive and explicit formulas for sequences

Consider the sequence 5, 8, 11, 14, 17, ...

What might the next number be?
John was trying to come up with a recursive formula to use that would model this sequence. Below is his work so far. Can you fill in the remaining work and find a recursive formula?





Recursive Formula
Paris wanted to outdo John and come up with an explicit formula, that way she could find any number in the sequence quickly. Her work is down below. Can you fill in the remaining work and find an explicit formula?





Explicit formula

In general,

______relies on proceeding terms.
______is based on fixed numbers, many times the first number in the sequence.
Explain John’s formula
Explain Paris’ formula

Find the first 4 numbers in the following sequences

for and
Term / n / / Sequence
1st / 0
2nd
3rd
4th
5th
for and
Term / n / / Sequence
1st
2nd
3rd
4th
5th
for and
Term / n / / Sequence
1st
2nd
3rd
4th
5th

Kody made up a recursive formula and used it to generate a sequence. He used B(n) to stand for the nth term of his recursive sequence.

What does mean?
What does mean?
If and write a possible recursive formula involving and that would generate 28 and 33 in the sequence.
What does mean?
What does mean?
Would it necessarily be the same as?

Consider a sequence given by the formula where

List the first five terms of the sequence
Write an explicit formula
Find and of the sequence

Lyric opens a bank account. The deal he makes with his mother is that if he doubles the amount that was in the account at the beginning of each month by the end of the month, she will add an additional $5 to the account at the end of the month.

Let represent the amount in the account at the beginning of the month. Assume that he does, in fact, double the amount every month. Write a recursive formula for the amount of money in his account at the beginning of the month

Home Work!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

For problems 1-4, list the first five terms of each sequence

For Problems 5-10, write a recursive formula for each sequence given or described below

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