Arithmetic Series Concepts and Calculations

The video tutorial explains how to determine the sum of a series given in sigma notation. It identifies the series as arithmetic, calculates the terms, and uses the formula for the sum of an arithmetic series. The tutorial also clarifies the correct method to find the number of terms in the series and provides a step-by-step calculation of the series sum.

What is the common difference in the arithmetic series given in the problem?

• 2

• 3

• 5

• 6

What is the first term of the series when n equals 21?

• 63

• 65

• 68

• 66

How do you calculate the common difference in an arithmetic series?

• Multiply any term by the next term

• Add any term to the next term

• Subtract any term from the next term

• Divide any term by the next term

What is the last term of the series when n equals 60?

• 180

• 182

• 185

• 190

How many terms are there in the series from n equals 21 to 60?

• 38

• 41

• 40

• 39

Why do we add one when calculating the number of terms in the series?

• To account for the last term

• To account for both the first and last terms

• To account for the middle term

• To account for the first term

What is the formula used to calculate the sum of an arithmetic series?

• S = n * (a1 + an)

• S = n/2 * (a1 + an)

• S = n * (a1 - an)

• S = n/2 * (a1 - an)

What is the sum of the series from n equals 21 to 60?

• 5000

• 5100

• 5050

• 4940

What is the value of a1 in the series?

• 71

• 68

• 65

• 63

What is the value of an in the series?

• 180

• 190

• 182

• 185