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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) a_{n1}+5, a_{1}=10
2) a_{n1}7, a_{1}=2
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PBL sources
http://www.purplemath.com
http://www.kutasoftware.com
http://www.khan academy.com
http://www. youtube.com
Above and beyond step 2
Peyton Baranowski
Mr. Rob
Algebra 1
Step 2
31714
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 Qsequence
VI Fibonacci sequence
awho found it
bWhere 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: a_{n}= a_{n1 }+ 2
Example 2:
0,3,6,9
In this pattern you add 3 to get the next term.
The equation would look like a_{n1}+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…
