Finite Geometric Series assignment
What is the value of the geometric series?
A
Which expression can be used to find the salary, in thousands, for the second year? Select all that apply.
A, C
Which of the following show a geometric series? Select all that apply.
A, E
The approximate salary, in thousands, earned each year for the first five years is $400, $420, $441, $463, and $486. Explain how you can evaluate the fifth partial sum. What does the fifth partial sum represent?
Add the five terms. Use the formula for the fifth partial sum. The fifth partial sum represents the total amount of money the athlete earns over the first five years.
Identify the formula that can be used to find the athlete's salary, in thousands of dollars, for year n?
B
Select the explicit formula for the sequence.
B
What is the series in summation notation?
B
Which can be used to find the eighth partial sum?
C
Which shows the partial sum, in thousands, of the first four terms in summation notation?
C
Which shows the terms of the series?
C
Evaluate each series. mc001-1.jpg mc002-1.jpg
C, A
Answer each question about the following geometric series: mc001-1.jpg How many terms are in the series?
D
The athlete's salary, in thousands, for the first two years is $400 and $400(1.05). Explain how to find her salary for each of the next three years. Do these values form a geometric sequence? Explain.
Find the third year's salary by multiplying the second year's salary by 1.05 Find the fourth year's salary by multiplying the third year's salary by 1.05. Find the fifth year's salary by multiplying the fourth year's salary by 1.05. The salaries form a geometric sequence because the athlete's salary changes by a common ratio of 1.05 each year.
What is the percent increase written as a decimal?
0.05
Identify the value of r and a1 for each geometric series.
1.5, 2, 0.5, 8
What is the last term of the series?
1536
The fifth partial sum, in thousands, is approximately
2210
How much money will the athlete earn over the first five years?
2210000
Evaluate the series. What is the sum?
255
What is the first term of the series?
3
Over the eight-year contract, the athlete would make approximately
3820000
0.25 + 1 + 4 + 16 + 64 Enter the values used in finding a partial sum.
4, 0.25, 5
How much will the athlete make, in thousands, during the first year?
400
The athlete's salary each year forms a geometric sequence. What is a1, in thousands? What is r?
400, 1.05
Find the first four terms, in thousands, of the geometric series. Round to the nearest thousand.
400, 420, 441, 463
A pro-athlete is offered an eight-year contract with a starting salary of $400,000. She will receive an annual increase of 5% for meeting certain goals. The athlete receives another offer of an eight-year contract with a starting salary of $425,000 and a 4% increase each year for meeting the same goals. Which offer should the athlete take? Explain.
The offer of $400,000 plus 5% per year earns approximately $3,820,000 in 8 years. The offer of $425,000 plus 4% per year earns approximately $3,916,000 in 8 years. The athlete should take the offer of $425,000 plus 4% because she will earn more money from this deal over 8 years.
Mia takes a job with a starting salary of $40,000 for the first year. She earns a 3% increase each year. Write an equation for the partial sum of the geometric sequence used to model the situation and explain what an, n, Sn, and r represent (use a_n to represent an).
The partial sum that models the situation is Sn=a1(1 - rn)/(1 - r). n = number of years Mia works this job an = Mia's salary during her nth year Sn = total amount Mia earns after n years r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase
Would you use the same method to find the eighth partial sum as you used to find the fifth partial sum? Why or why not?
Would you use the same method to find the eighth partial sum as you used to find the fifth partial sum? Why or why not?
