Using Inductive ReasoningNumber Patterns

Inductive reasoningObserve a pattern and come up

with general principles ( A Rule or Formula)

Today we will look at how observations are turned in to Mathematical rules

First; Some Vocab Number Sequence

Terms

Arithmetic Sequence

Geometric Sequence

- A list of numbers. There’s a 1st number, a 2nd number… etc

- The name of one of the numbers in the sequence

- There is a common difference (you + or – a number each time)

- There is a common Ratio (you x or ÷ a number each time)

Sequences Arithmetic

3,7,11,15,19…

Difference from one term to another is;

101, 92, 83, 74…

Difference from one term to another is;

Geometric 7, 21, 63, 189…

The ration you multiply by each time is;

276, 138, 69…

The ratio you multiply by each time is;

Successive Differences Sometimes the differences between

numbers follow a pattern Use a Tree scheme to figure out the

pattern of the differences. Continue until you get a constant difference

The Sum of “n” odd counting numbers

n= # of terms1 = 12 n=11+3 = 22 n=21+3+5 = 32 n=31+3+5+7 = 42 n=41+3+5+7+9 = 52

n=5

1+3+5+7+9+11= 62 n=6

Find the sum of “n” odd counting numbers

2n-1 = n2

The sum of 8 odd counting numbers1, 3, 5…. (2n-1)← the last term

n2 = the sum of those #s