# Above and beyond recursive sequences presentation

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# Above and beyond PBL handout

Name:_______                                                                             Date:_____

Determine if the sequence is arithmetic. If it is, find the common difference.

1) ?3, ?23, ?43, ?63, …

2) 30, 40, 50, 60 …

Given the First term and the formula find the fist 3 terms.

1) an-1+5, a1=10

2) an-1-7, a1=2

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# Above and beyond step 2

Peyton Baranowski
Mr. Rob
Algebra 1
Step 2
3-17-14

Outline

I-     Introduction

II-   What is a Recursive sequence

a-    Types
b-    How to solve
c-     What’s with the symbols

III- Popular sequences
a-    Fibonacci
b-  Hoftars Q-sequence

VI- Fibonacci sequence
a-who found it
b-Where can you find it

IV- Practice
a-    Example problem
b-    Handout
V- Conclusion

# Above and beyond step 1

Recursive sequences: a set of numbers that follow a pattern.

You can find terms that are not listed by finding the pattern or solving a problem.

Example:

2,4,6,8,10

in this pattern you add 2 to the term before the term your solving for to get the next number.

So the next number is 12.

The equation would look like this: an= an-1 + 2

Example 2:

0,-3,-6,-9

In this pattern you add -3 to get the next term.

The equation would look like  an-1+-3

So the next terms are -12,-15, -18

It wasn’t till the late 1800’s to the early 1900’s that recursive sequences where studied in depth. This is where the name recursive sequence arose.

Fibonacci sequence: the Fibonacci sequence was discovered by Leonardo Fibonacci over a millennium ago this was around the 200bc. The Fibonacci sequence can be found almost anywhere some say it can be found in the Mona Lisa.

How was the Fibonacci sequence discovered: it’s thought the sequence first arose in in 200 BC by Pingala on possible patterns in poetry formed by syllables of different lengths. In 1202 Leonardo Fibonacci discovered the sequence when he was trying to find a mathematical solution concerning the breeding of rabbits. In 1611 Johannes Kepler found the sequence

 Trying to find approximations to the pentagon. Recurrence Relations( recursive sequences)  has been understood since the early 1600’s; however, it has only been widely discussed over a couple of decades. Where can you find the Fibonacci sequence? The Mona Lisa Hurricanes Flowers Plants Animal Breeding Seashells Starfish Pentagons The Human finger The human arm The human ear Pine cones Pineapples The human eye And more…