2. Inductive reasoning
Observe 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
3. First; Some Vocab
Number Sequence - A list of numbers. There’s a 1st
number, a 2nd number… etc
Terms - The name of one of the numbers in
the sequence
Arithmetic Sequence - There is a common
difference (you + or – a
number each time)
Geometric
- There is a common Ratio
Sequence (you x or ÷ a number
each time)
4. Sequences
Arithmetic Geometric
3,7,11,15,19… 7, 21, 63, 189…
Difference from one The ration you
term to another is; multiply by each
time is;
101, 92, 83, 74… 276, 138, 69…
Difference from one The ratio you multiply
term to another is; by each time is;
5. 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
6. The Sum of “n” odd
counting numbers
Find the sum of “n” odd counting
numbers
n= # of terms
1 = 12 n=1 2n-1 = n2
1+3 = 22 n=2
1+3+5 = 32 n=3 The sum of 8 odd counting
1+3+5+7 = 42 n=4 numbers
1+3+5+7+9 = 52 n=5 1, 3, 5…. (2n-1)← the last term
1+3+5+7+9+11= 62 n=6
n2 = the sum of those #s
