Exploring Geometric Series

What is a geometric series?

• A geometric series is the product of the terms of a geometric sequence.

• A geometric series is a sequence of geometric shapes.

• A geometric series is the sum of the terms of a geometric sequence.

• A geometric series is a type of polynomial expression.

Identify the geometric series: 2, 6, 18, 54.

• 2, 6, 18, 54 is a geometric series with a common ratio of 3.

• 1, 3, 9, 27 is a geometric series with a common ratio of 3.

• 5, 10, 20, 40 is a geometric series with a common ratio of 2.

• 2, 4, 8, 16 is a geometric series with a common ratio of 2.

Calculate the sum of the first 5 terms of the series: 3, 6, 12, 24.

• 100

• 75

• 93

• 60

What is the nth term of the geometric series: 5, 15, 45, ...?

• 5 + 3^(n-1)

• 5 * 2^(n-1)

• 5 * 3^(n-1)

• 10 * 3^(n-1)

Determine if the series 1, 1/2, 1/4, 1/8 converges or diverges.

• diverges

• oscillates

• is undefined

• converges

Find the sum of the infinite geometric series: 4 + 2 + 1 + ...

• 12

• 8

• 10

• 6

What is the common ratio in the series: 7, 21, 63, ...?

• 4

• 3

• 2

• 5

If the first term of a geometric series is 10 and the common ratio is 0.5, what is the 6th term?

• 5

• 0.625

• 1.25

• 0.3125

Explain how geometric series can be applied in finance.

• Geometric series are used to calculate stock prices directly.

• Geometric series are used to calculate the present value of annuities and growing cash flows in finance.

• Geometric series are primarily used for budgeting and expense tracking.

• Geometric series help in determining the interest rates for loans.

Calculate the sum of the geometric series: 1 + 1/3 + 1/9 + 1/27.

• 1/2

• 40/27

• 1/4

• 2/3