Calculating Finite Geometric Series Sums

This video tutorial explains how to find the sum of a finite geometric series. It begins with a simple example, demonstrating how to manually add terms to find the sum. The tutorial then introduces a formula for calculating partial sums, which is useful for larger series. Several examples are provided, including the use of summation notation for large series. The video concludes with a final example, reinforcing the concepts and methods discussed.

What is the sum of the first five terms of the series 4, 8, 16, 32, 64?

• 132

• 120

• 128

• 124

What is the common ratio in the series 4, 8, 16, 32, 64?

• 3

• 2

• 1

• 4

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

• a₁(1 - rⁿ) / (1 + r)

• a₁(1 + rⁿ) / (1 + r)

• a₁(1 - rⁿ) / (1 - r)

• a₁(1 + rⁿ) / (1 - r)

Using the formula, what is the sum of the first five terms of the series 4, 8, 16, 32, 64?

• 124

• 120

• 128

• 132

What is the common ratio in the series 2, 6, 18, 54, 162, 486?

• 4

• 3

• 5

• 2

What is the sum of the first six terms of the series 2, 6, 18, 54, 162, 486?

• 744

• 736

• 728

• 720

In the series 27, 9, 3, what is the common ratio?

• 1/3

• 1/5

• 1/2

• 1/4

What is the approximate sum of the first 30 terms of the series 27, 9, 3, ...?

• 43.5

• 42.5

• 41.5

• 40.5

What is the common ratio in the series 4, 8, 16, ...?

• 1

• 2

• 3

• 4

What is the sum of the first 20 terms of the series 4, 8, 16, ...?

• 4,194,500

• 4,194,400

• 4,194,300

• 4,194,600