Understanding Arithmetic Series

This video tutorial explains how to prove the formula for the sum of an arithmetic series. It begins by distinguishing between an arithmetic sequence and an arithmetic series, using an example to illustrate the concept. The tutorial then demonstrates how to calculate the sum of a series using a specific formula, which involves averaging the first and last terms and multiplying by the number of terms. Finally, the video derives the formula for the sum of an arithmetic series, showing the step-by-step process of adding terms and factoring out common elements.

What is the common difference in the arithmetic sequence 5, 8, 11, 14, 17?

• 2

• 5

• 3

• 4

How do you convert an arithmetic sequence into a series?

• Divide all terms

• Multiply all terms

• Add all terms

• Subtract all terms

What is the sum of the first five terms of the sequence 5, 8, 11, 14, 17?

• 45

• 60

• 50

• 55

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

• (First term - Last term) * n

• (First term * Last term) / n

• (First term + Last term) / 2 * n

• (First term + Last term) * n

What is the expression for the second term in an arithmetic series?

• First term * d

• First term - d

• First term + 2d

• First term + d

How do you express the third term in terms of the first term and common difference?

• First term - 2d

• First term * 2d

• First term + 2d

• First term + 3d

What happens when you add the equations from left to right and right to left?

• The terms cancel out

• The terms are halved

• The terms double

• The terms remain the same

What is the greatest common factor (GCF) in the final formula derivation?

• a sub n

• a sub 1

• a sub 1 + a sub n

• d

How many terms of a sub 1 + a sub n are there in the final expression?

• n

• 2n

• n/2

• n+1

What is the final step in deriving the formula for the sum of an arithmetic series?

• Multiply by n

• Add d

• Subtract d

• Divide by 2