Download presentation

Published byWesley Armstrong Modified over 6 years ago

1
Sequences and Series It’s all in Section 9.4a!!!

2
**“sequence” will refer to**

Sequence – an ordered progression of numbers – examples: 1. Finite Sequence 2. Infinite Sequences 3. (unless otherwise specified, the word “sequence” will refer to an infinite sequence) 4. which is sometimes abbreviated Notice: In sequence (2) and (3), we are able to define a rule for the k-th number in the sequence (called the k-th term).

3
Practice Problems Find the first 6 terms and the 100th term of the sequence in which Note: This is an explicit rule for the k-th term

4
Practice Problems Another way to define sequences is recursively, where we find each term by relating it to the previous term. Find the first 6 terms and the 100th term for the sequence defined recursively by the following conditions: for all n > 1. The sequence: The pattern???

5
**Definition: Arithmetic Sequence**

A sequence is an arithmetic sequence if it can be written in the form for some constant d. The number d is called the common difference. Each term in an arithmetic sequence can be obtained recursively from its preceding term by adding d: (for all n > 2).

6
Practice Problems For each of the following arithmetic sequences, find (a) the common difference, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 1. (a) The difference ( d ) between successive terms is 4. (b) (c) (d)

7
Practice Problems For each of the following arithmetic sequences, find (a) the common difference, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 2. (a) The difference ( d ) between successive terms is –3. (b) (c) (d)

8
Practice Problems For each of the following arithmetic sequences, find (a) the common difference, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 3. Is this sequence truly arithmetic??? Difference between successive terms: We do have a common difference!!!

9
Practice Problems For each of the following arithmetic sequences, find (a) the common difference, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 3. (a) The difference ( d ) between successive terms is ln(2). (b)

10
Practice Problems For each of the following arithmetic sequences, find (a) the common difference, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 3. (c) (d)

11
Geometric Sequences

12
**Definition: Geometric Sequence**

A sequence is a geometric sequence if it can be written in the form for some non-zero constant r. The number r is called the common ratio. Each term in a geometric sequence can be obtained recursively from its preceding term by multiplying by r : (for all n > 2).

13
Guided Practice For each of the following geometric sequences, find (a) the common ratio, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 1. (a) The ratio ( r ) between successive terms is 2. (b) (c) (d)

14
Guided Practice For each of the following geometric sequences, find (a) the common ratio, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 2. (a) Apply a law of exponents: (b)

15
Guided Practice For each of the following geometric sequences, find (a) the common ratio, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 2. (c) (d)

16
Guided Practice For each of the following geometric sequences, find (a) the common ratio, (b) the tenth term, (c) a recursive rule for the n-th term, and (d) an explicit rule for the n-th term. 3. (a) The ratio ( r ) between successive terms is –1/2. (b) (c) (d)

17
**Guided Practice The second and fifth terms of a sequence are 3 and 24,**

respectively. Find explicit and recursive formulas for the sequence if it is (a) arithmetic and (b) geometric. If the sequence is arithmetic: Explicit Rule: Recursive Rule:

18
**Guided Practice The second and fifth terms of a sequence are 3 and 24,**

respectively. Find explicit and recursive formulas for the sequence if it is (a) arithmetic and (b) geometric. If the sequence is geometric: Explicit Rule: Recursive Rule:

Similar presentations

© 2022 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google