Download presentation

Presentation is loading. Please wait.

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:

Similar presentations

OK

Algebra 1 Find the common ratio of each sequence. a. 3, –15, 75, –375,... 3–1575–375 (–5) (–5) (–5) The common ratio is –5. b. 3, 3232 3434 3838,,,...

Algebra 1 Find the common ratio of each sequence. a. 3, –15, 75, –375,... 3–1575–375 (–5) (–5) (–5) The common ratio is –5. b. 3, 3232 3434 3838,,,...

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on business cycle theories Ppt on girl child abortion Ppt on search engine optimisation Ppt on adobe photoshop tools Ppt on elections in india download song Ppt on save environment speech Ppt on amplitude shift keying modem Ppt on producers consumers and decomposers in the forest Close reading elementary ppt on cells Ppt on production planning and inventory control