1. 11.1 Mathematical Patterns

2. Ex 1
Start with a square with sides 1 unit long. On the right side, add on a square of the same size. Continue adding one square at a time in this way. Draw the first four figures.

3. Ex 2
Write the number of 1 unit segments in each figure from ex 1 as a sequence.

4. Ex 3
Describe the pattern formed and find the next three terms. 243, 81, 27, 9, …

5. Ex 4
Suppose you drop a ball from a height of 100 cm. It bounces back to 80% of its previous height. How high will it go after its fifth bounce?

6. We can use a variable with positive integer subscripts to represent the terms in a sequence:
a1 a2 a3 – first, second and third terms
an-1: n – 1 term
an : nth term
an+1 : n + 1 term
n is the term number

7. Recursive formula
Defines the terms in a sequence by relating each term to the ones before it. (ex 4 was recursive b/c the height was 80% of its previous height)
Formula would be an = 0.80an-1 where
a1 = 100

8. Ex 5 Describe the pattern of the sequence: 2, 6, 18, 54, 162, …
Write a recursive function.
Find the 6th and 7th terms.
Find the value of a10

9. Explicit formula Expresses the nth term in terms of n
Finding the value of a term without knowing the preceding term.
(Find a link between the term number and the term value.)

10. EX 6 Write a formula.
2, 6, 12, 20, …

11. Ex 7 Write a formula
3, 5, 7, 9, …

12. Ex 8 Term a1 a2 a3 a4 Length of side 1 2 3 4 perimeter 5 10 15 20
For each sequence, find the next term and the 20th term.
Write an explicit formula for each sequence.
n = the term number

13. Ex 9
Write the first six terms of the area of squares that have side lengths 1, 2, 3, etc.
Write an explicit formula.

14. Ex 10
Write a formula for

15. Ex 11
Write a formula for: