Presentation is loading. Please wait.

Presentation is loading. Please wait.

Grade 11 Functions (MCR3U)

Published byShauna Snow Modified over 6 years ago

Similar presentations

Presentation on theme: "Grade 11 Functions (MCR3U)"— Presentation transcript:

1 Grade 11 Functions (MCR3U)
Unit 5: Pascal’s Triangle, Binomial Theorem, Sequences & Series Arithmetic Sequences Mr. Choi © 2018 E. Choi – MCR3U - All Rights Reserved

2 Arithmetic Sequence {a, a+d, a+2d, a+3d,...}
A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence. In an arithmetic sequence, the first term t1, is denoted as a. Each term after the first is found by adding a constant, called the common difference, d, to the preceding term. The list then becomes . {a, a+d, a+2d, a+3d,...} Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

3 Arithmetic Sequences Formulas
In general: {a, a+d, a+2d, a+3d,...} Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

4 Example 1 – Arithmetic Sequence
Given the formula for the term, find Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

5 Example 2 – Finding Formula for the nth term
Find the formula for the term, , and find that determines the following arithmetic sequence {8, 12, 16, 20, ...}. Method 2 19 19 n n 19 19 Explicit formula Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

6 Example 3 – Find number of terms in the sequence
How many terms are there in the following sequences? {-3, 2, 7, ..., 152}. There are 32 terms in the sequence. Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

7 Example 4 – Find the terms in the sequence
In an arithmetic sequence, t7 = 121 and t 15 = Find the first 3 terms of the sequence and 2 - 1 Substitute into (1) (1) (2) Therefore the sequences are: 67, 76, 85, ... Arithmetic Sequences Explicit formula © 2018 E. Choi – MCR3U - All Rights Reserved

8 Example 5 – Find the terms in the sequence
In an arithmetic sequence, t7 = 121 and t 15 = Find the first 3 terms of the sequence and METHOD 2 To find a, we use the same thinking process!! t1 = 121+(1-7)d tn=121+(n-7)d Therefore the sequences are: 67, 76, 85, ... Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

9 Example 6 – Applications of Arithmetic sequence
Find the general term of the following arithmetic sequence OR (5x - 3) (-2x - 1) Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

10 Homework: Text Book: P. 385 #1 - 12 Work Sheet:
Check the website for updates Extra questions: Solve the following equation How many consecutive natural numbers, starting with 1, need to be added to produce a sum of 153? Answers: 40 terms, y = 1 17 Arithmetic Sequences © 2018 E. Choi – MCR3U - All Rights Reserved

11 End of Lesson Arithmetic Sequences
© 2018 E. Choi – MCR3U - All Rights Reserved

Download ppt "Grade 11 Functions (MCR3U)"

Similar presentations

Choi 2012 Arithmetic Sequence A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence.

Choi 2012 Arithmetic Sequence A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence.
Arithmetic Sequences and Series Unit 10.2. Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant.

Arithmetic Sequences and Series Unit Definition Arithmetic Sequences – A sequence in which the difference between successive terms is a constant.
Section 11.2 Arithmetic Sequences

Section 11.2 Arithmetic Sequences
4.7 Arithmetic Sequences A sequence is a set of numbers in a specific order. The numbers in the sequence are called terms. If the difference between successive.

4.7 Arithmetic Sequences A sequence is a set of numbers in a specific order. The numbers in the sequence are called terms. If the difference between successive.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 10 Further Topics in Algebra.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 10 Further Topics in Algebra.
Geometric Sequences Section 3.2.1.

Geometric Sequences Section
Choi Geometric Sequence A sequence like 3, 9, 27, 81,…, where the ratio between consecutive terms is a constant, is called a geometric sequence. In a.

Choi Geometric Sequence A sequence like 3, 9, 27, 81,…, where the ratio between consecutive terms is a constant, is called a geometric sequence. In a.
12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.

12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.
12.2: Analyze Arithmetic Sequences and Series HW: p.806-807 (4, 10, 12, 14, 24, 26, 30, 34)

12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)
2, 4, 6, 8, … a1, a2, a3, a4, … Arithmetic Sequences

2, 4, 6, 8, … a1, a2, a3, a4, … Arithmetic Sequences
Standard 22 Identify arithmetic sequences Tell whether the sequence is arithmetic. a. –4, 1, 6, 11, 16,... b. 3, 5, 9, 15, 23,... SOLUTION Find the differences.

Standard 22 Identify arithmetic sequences Tell whether the sequence is arithmetic. a. –4, 1, 6, 11, 16,... b. 3, 5, 9, 15, 23,... SOLUTION Find the differences.
Notes Over 11.2 Arithmetic Sequences An arithmetic sequence has a common difference between consecutive terms. The sum of the first n terms of an arithmetic.

Notes Over 11.2 Arithmetic Sequences An arithmetic sequence has a common difference between consecutive terms. The sum of the first n terms of an arithmetic.
Arithmetic and Geometric Sequences Finding the nth Term 2,4,6,8,10,…

Arithmetic and Geometric Sequences Finding the nth Term 2,4,6,8,10,…
Arithmetic Sequences & Series. Arithmetic Sequence: The difference between consecutive terms is constant (or the same). The constant difference is also.

Arithmetic Sequences & Series. Arithmetic Sequence: The difference between consecutive terms is constant (or the same). The constant difference is also.
Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.

Arithmetic Sequences In an arithmetic sequence, the difference between consecutive terms is constant. The difference is called the common difference. To.
Arithmetic Sequences Sequence is a list of numbers typically with a pattern. 2, 4, 6, 8, … The first term in a sequence is denoted as a 1, the second term.

Arithmetic Sequences Sequence is a list of numbers typically with a pattern. 2, 4, 6, 8, … The first term in a sequence is denoted as a 1, the second term.
Chapter 11 Sequences and Series

Chapter 11 Sequences and Series
Copyright © Cengage Learning. All rights reserved. Sequences and Series.

Copyright © Cengage Learning. All rights reserved. Sequences and Series.
Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

Unit 9: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.
Grade 10 Academic (MPM2D) Unit 3: Algebra & Quadratic Models Product of Binomials & Polynomials Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

Grade 10 Academic (MPM2D) Unit 3: Algebra & Quadratic Models Product of Binomials & Polynomials Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

Similar presentations

Ads by Google