We appreciate your visit to A company that manufactures smartphone cases plans to increase production by an additional 120 cases each month for the next 24 months Last month they. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Using arithmetic sequence concepts, it is found that:
a) Yes, it is an arithmetic sequence. as the common difference is constant.
b) The sequence is: [tex]a_n = 120n + 1930[/tex]
c) The company plans to produce 82,320 cases during the next 24 months.
What is an arithmetic sequence?
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
Item a:
The production will be increased by an additional 120 cases each month for the next 24 months, which means that the common difference is constant, so yes, it is an arithmetic sequence.
Item b:
- Last month they manufactured 1930 smartphone cases, hence in this month they will manufacture 2050 cases, hence [tex]a_1 = 2050[/tex].
- Increases by 120 a month, hence [tex]d = 120[/tex].
Then, the sequence is:
[tex]a_n = a_1 + (n - 1)d[/tex]
[tex]a_n = 2050 + 120(n - 1)[/tex]
[tex]a_n = 120n + 1930[/tex]
Item c:
[tex]a_1 = 2050[/tex]
[tex]a_24 = 120(24) + 1930 = 4810[/tex]
Then:
[tex]S_{24} = 12(2050 + 4810) = 82320[/tex]
The company plans to produce 82,320 cases during the next 24 months.
You can learn more about arithmetic sequence concepts at https://brainly.com/question/26053884
Thanks for taking the time to read A company that manufactures smartphone cases plans to increase production by an additional 120 cases each month for the next 24 months Last month they. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
