Using inductive reasoning
- 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