quired next three terms are 4. 3, 4, 7, 8, 11, ... 5. 1,8, 27, 64, 125, 216, 343, 512, 729.....

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter6: Exponential Functions And Sequences
Section6.7: Recursively Defined Sequence
Problem 53E
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Question
ANSWER 4 to 5 only
ACTIVITY 2
Sequences and Patterns
1. Write the next three terms for the given sequences and patterns.
1. 1, 2, 4, 8, 16, ...
Solution:
Given sequence is
1, 2, 4, 8, 16, ...
The following pattern is observed.
1x2=2
2x2= 4
4x2=8
8x2= 16
The next three terms are-
16 x 2= 32
32 x 2= 64
64x 2= 128
Required next three terms are-
32, 62, 128
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
2.
Solution:
Given sequence is
1, 1, 2, 3, 5, 8, 13, 21, 34,...
The following pattern is observed.
1+1=2
2+1=3
3+2=5
5+3=8
The next three terms are
34+ 21 55
55+34= 89
89+55= 144
Required next three terms are
4, 10, 16, 22, 28, ...
3.
Solution:
Given sequence is
The following pattern is observed.
4 + 6 = 10
10+ 6 = 16
16+6 = 22
22+6 = 28
The next three terms are
28 + 6 = 34
34 + 6 = 40
40+ 6 = 46
55,89,144
4, 10, 16, 22, 28....
quired next three terms are
4.
3, 4, 7, 8, 11, ...
5.
1, 8, 27, 64, 125, 216, 343, 512, 729, ...
||
Transcribed Image Text:ACTIVITY 2 Sequences and Patterns 1. Write the next three terms for the given sequences and patterns. 1. 1, 2, 4, 8, 16, ... Solution: Given sequence is 1, 2, 4, 8, 16, ... The following pattern is observed. 1x2=2 2x2= 4 4x2=8 8x2= 16 The next three terms are- 16 x 2= 32 32 x 2= 64 64x 2= 128 Required next three terms are- 32, 62, 128 1, 1, 2, 3, 5, 8, 13, 21, 34, ... 2. Solution: Given sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34,... The following pattern is observed. 1+1=2 2+1=3 3+2=5 5+3=8 The next three terms are 34+ 21 55 55+34= 89 89+55= 144 Required next three terms are 4, 10, 16, 22, 28, ... 3. Solution: Given sequence is The following pattern is observed. 4 + 6 = 10 10+ 6 = 16 16+6 = 22 22+6 = 28 The next three terms are 28 + 6 = 34 34 + 6 = 40 40+ 6 = 46 55,89,144 4, 10, 16, 22, 28.... quired next three terms are 4. 3, 4, 7, 8, 11, ... 5. 1, 8, 27, 64, 125, 216, 343, 512, 729, ... ||
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