Algebra

Lab and Forum post. Ignore the respond to two students posts on the forum post section.

  

MA1310: Week 9 Sequences and Notations

This lab requires you to:

· Find particular terms of a sequence from the general term.

· Use recursion formulas.

· Use factorial notation.

· Use summation notation.

· Find the common difference for an arithmetic sequence.

· Write terms of an arithmetic sequence.

· Use the formula for the general term of an arithmetic sequence.

· Use the formula for the sum of the first n terms of an arithmetic sequence.

· Find the common ratio of a geometric sequence.

· Write terms of a geometric sequence.

· Use the formula for the general term of a geometric sequence.

· Use the formula for the sum of the first n terms of a geometric sequence.

Answer the following questions to complete this lab:

1. Describe an arithmetic sequence in two sentences.

2. Describe a geometric sequence in two sentences.

3. The sequence shown below is defined using a recursion formula. Write the first four terms of the sequence.

a1 = 13 and an = an-1 + 8 for n

4. A company offers a starting yearly salary of $33,000 with a raise of $2,500 per year. Find the total salary over a ten-year period.

5. Suppose you save $1 the first day of a month, $5 the second day, $25 the third day, and so on. That is, each day you save five times as much as you did the day before. What will you put aside for savings on the eighth day of the month?

Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab9.1_Date.

Evaluation Criteria:

· Did you show the relevant steps in doing problems?

· Did you write thorough explanations for the short-answer questions?

· Did you submit your answers in an organized fashion that was legible and easy to follow?

· Were the answers correct?

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MA1310:Week 9 Solving Real-Life Problems Using Sequences

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Sequences are among the oldest objects of mathematical investigation, having been

studied for over 3,500 years. Arithmetic and geometric sequences appear in the Rhind

papyrus, a mathematical text containing 85 problems copied around 1650 BC by

Egyptian scribe Ahmes from an earlier work. When algebra became sufficiently

developed in the 1500s, more complicated problems were solved by using sequences. In

the modern world, sequences have many real-life applications, such as predicting world

population prospects.

Let’s discuss the following old English children’s rhyme from one of the Rhind papyrus

texts:

As I was going to St. Ives

I met a man with seven wives

Each wife had seven sacks

Each sack had seven cats

Each cat had seven kits [kittens]

Kits, cats, sacks, wives

How many were going to St. Ives?

• Assuming that the speaker and the cat fanciers met by traveling in opposite

directions, what is the answer?

• How many kittens are being transported?

• Kits, cats, sacks, wives; how many?

You are required to:

• Answer the above questions one by one. Explain if you can connect your answers to

sequences in any way.

• Pick a real-life application using sequences, preferably from the financial

applications, and state it in a few sentences.

• Describe in three sentences what your strategy will be to solve your application
problem.

MA1310: Week 9 Solving Real-Life Problems Using Sequences

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Participation Requirements:

• Respond to two other peers’ initial posts with appropriate replies using at least

three sentences.

• State in your responses why you agree or disagree with your peers’ posts.

• Include in your responses tips to solve such problems in connection with sequences.

Evaluation Criteria:

• Did you accurately analyze the stated problem?

• Did you describe an application accurately?

• Did you reply to all parts of the problem statement?

• Did you reply to two other students’ posts with appropriate analysis?