Geometric Series and Salary Calculations

Geometric Series and Salary Calculations

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to calculate the total earnings over five years for a job with an initial salary of $55,000 and an annual increase of 6%. It introduces the concept of a geometric series, where each term is multiplied by a constant ratio, in this case, 1.06. The tutorial walks through the formula for the sum of a geometric series and demonstrates the calculation step-by-step, emphasizing the importance of order of operations. The final result shows the total earnings over five years, highlighting the growth due to the geometric progression.

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20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial annual salary in the given problem?

$60,000

$55,000

$50,000

$65,000

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the annual pay increase percentage in the problem?

8%

7%

6%

5%

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the salary increment scenario considered a geometric series?

Because the salary increases by a fixed amount each year.

Because the salary increases by a fixed percentage each year.

Because the salary decreases by a fixed percentage each year.

Because the salary remains constant each year.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the constant ratio used in this geometric series?

1.07

1.05

1.06

1.08

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the constant ratio expressed as a percentage?

108%

107%

106%

105%

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula used to calculate the sum of a geometric series?

Sum = a * (1 - r^n) / (1 - r)

Sum = a * (r^n - 1) / (r - 1)

Sum = a * (1 + r^n) / (1 + r)

Sum = a * (r^n + 1) / (r + 1)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of 'a' in the formula for this problem?

$65,000

$60,000

$55,000

$50,000

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