The Sum of Terms of a Sequence Suppose that a virus enters a community and the number of new infections each week forms an arithmetic sequence. If there were 6 cases the first week and, in each week thereafter, 4 more new cases than the week before, then the sequence a, = 6, 10, 14, 18, 22, ... of new cases in the wth week can be described with the formulas below. Recursive Formula Explicit Formula 4₂-6+ (8-1)4-6+4(x-1) It is important to keep track of the total number of cases, not just new cases. The table and graph below show the first five terms of the sequence and the cumulative totals. Week New Cases Total Number Infected 1 6 2 6+10=16 6+10+14-30 6+10+14+18= 48 6+10+14+18+22= 70 infected 60 40 30 new cases 20 10 0 1 2 3 4 5 6 7 8 Week 3 5 Number of People 10 21%2 14 18 22 1) Complete the sentence: "This example reminds me of..." 2) Describe the mathematical difference between the red points (new cases) and the blue points (infected) on the graph.
The Sum of Terms of a Sequence Suppose that a virus enters a community and the number of new infections each week forms an arithmetic sequence. If there were 6 cases the first week and, in each week thereafter, 4 more new cases than the week before, then the sequence a, = 6, 10, 14, 18, 22, ... of new cases in the wth week can be described with the formulas below. Recursive Formula Explicit Formula 4₂-6+ (8-1)4-6+4(x-1) It is important to keep track of the total number of cases, not just new cases. The table and graph below show the first five terms of the sequence and the cumulative totals. Week New Cases Total Number Infected 1 6 2 6+10=16 6+10+14-30 6+10+14+18= 48 6+10+14+18+22= 70 infected 60 40 30 new cases 20 10 0 1 2 3 4 5 6 7 8 Week 3 5 Number of People 10 21%2 14 18 22 1) Complete the sentence: "This example reminds me of..." 2) Describe the mathematical difference between the red points (new cases) and the blue points (infected) on the graph.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter13: Sequences And Series
Section13.CT: Chapter Test
Problem 6CT
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Question
Transcribed Image Text:The Sum of Terms of a Sequence
Suppose that a virus enters a community and the number of new
infections each week forms an arithmetic sequence. If there were 6
1) Complete the sentence:
"This example reminds me of..."
cases the first week and, in each week thereafter, 4 more new cases than
the week before, then the sequence a, = 6, 10, 14, 18, 22, . of new cases
in the nth week can be described with the formulas below.
2) Describe the mathematical difference between the
red points (new cases) and the blue points (infected)
on the graph.
Recursive Formula
Explicit Formula
Ja,-6
[.- +4, >0
It is important to keep track of the total number of cases, not just
new cases. The table and graph below show the first five terms of
the sequence and the cumulative totals.
a, = 6+ (n - 1)4 = 6 + 4(n – 1)
Week
New Cases
Total Number Infected
1
6.
6
2
10
6+ 10 = 16
3
14
6 + 10 + 14 = 30
4
18
6+ 10 + 14 + 18 = 48
5
22
6 + 10 + 14 + 18 + 22 = 70
70
infected
60
50
40
30
new cases
20
10
0 12 3 4 5 6 7 8
Week
Number of People
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