Download presentation

Presentation is loading. Please wait.

Published byJody Hampton Modified over 7 years ago

1
Lesson #8.6: Geometric Sequence Objective: SWBAT form geometric sequences and use formulas when describing sequences

2
8.6 – Geometric Sequences Recall the sequence 2, 5, 8, 11, 14, … What did we say was the Common Difference? (+3) This type of a sequence is called an Arithmetic Sequence: a sequence formed by adding or subtracting a fixed # to the previous term

3
8.6 – Geometric Sequences Now look at the sequence 3, 15, 75, 375, … What is happening here? (x5)

4
8.6 – Geometric Sequences The last sequence is called a Geometric sequence: multiplying a term in a sequence by a fixed # to find the next term Common ratio: the fixed # that you continuously multiply by You always have to multiply by some # in a geometric sequence; if division is being used, remember you can MULTIPLY BY THE RECIPROCAL.

5
Definitions A sequence is a set of numbers, called terms, arranged in some particular order.

6
8.6 – Geometric Sequences Find the common ratio: 5, -10, 20, -40, …

7
Examples: Find the common ratio of the following: 1) 1, 2, 4, 8, 16,... r = 2 2) 27, 9, 3, 1, 1/3,... r = 1/3 3) 3, 6, 12, 24, 48,... r = 2 4) 1/2, -1, 2, -4, 8,... r = -2 8.6 – Geometric Sequences

8
Examples: Find the next term in each of the previous sequences. 1) 1, 2, 4, 8, 16,... 32 2) 27, 9, 3, 1, 1/3,... 1/9 3) 3, 6, 12, 24, 48,... 96 4) 1/2, -1, 2, -4, 8,... -16

9
8.6 – Geometric Sequences To determine if it is arithmetic or geometric, look at the common change. Arithmetic = added or subtracted Geometric = multiplied

10
Let's play guess the sequence!: I give you a sequence and you guess the type. 1. 3, 8, 13, 18, 23,... 2. 1, 2, 4, 8, 16,... 3. 24, 12, 6, 3, 3/2, 3/4,... 4. 55, 51, 47, 43, 39, 35,... 5. 2, 5, 10, 17,... 6. 1, 4, 9, 16, 25, 36,...

11
Answers! 1) Arithmetic, the common difference d = 5 2) Geometric, the common ratio r = 2 3) Geometric, r = 1/2 4) Arithmetic, d = -4 5) Neither, why? (How about no common difference or ratio!) 6) Neither again! (This looks familiar, could it be from geometry?)

12
This is important! Arithmetic formula: a n = a 1 + (n - 1)d A(n) = nth term a1 = first term d = common DIFFERENCE

13
8.6 – Geometric Sequences Geometric Formula A(n) = a * r A(n) = nth term a = first term r = common ratio n = term number n - 1

14
8.6 – Geometric Sequences Find the 10th term in A(n) = 5 * (-2) n - 1

15
Sample problems: Find the first four terms and state whether the sequence is arithmetic, geometric, or neither. 1) a n = 3n + 2 2) a n = n 2 + 1 3) a n = 3*2 n

16
Answers: 1) a n = 3n + 2 To find the first four terms, in a row, replace n with 1, then 2, then 3 and 4 Answer: 5, 8, 11, 14 The sequence is arithmetic! d = 3

17
2) a n = n 2 + 1 To find the first four terms, do the same as above! Answer: 2, 5, 10, 17 The sequence is neither. Why? 8.6 – Geometric Sequences

18
3) a n = 3*2 n Ditto for this one ( got it by now?) Answer: 6, 12, 24, 48 The sequence is geometric with r = 2 8.6 – Geometric Sequences

19
Find a formula for each sequence. 1) 2, 5, 8, 11, 14,... a 1 = 2 d = 3 Work: It is arithmetic! So use the arithmetic formula you learned! a 1 = 2, look at the first number in the sequence! d = 3, look at the common difference! Therefore, a n = 2 + (n - 1)3 and simplifying yields : a n = 3n -1 ( tada!) Try putting in 1, then 2, then 3, etc. and you will get the sequence! 8.6 – Geometric Sequences

Similar presentations

© 2023 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