Understanding Sigma Notation and Arithmetic Series

The video tutorial explains how to write sigma notation for a finite arithmetic series and calculate its sum. It begins by identifying the pattern in the series, derives the formula for the nth term, and simplifies it. The tutorial then determines the upper limit of the index and calculates the sum using the arithmetic series formula. The process is broken down into clear steps, making it easy to follow and understand.

What is the common difference in the given series?

• 3

• 5

• 7

• 9

Which term is the first in the series?

• 5

• 17

• 7

• 12

What is the formula for the nth term in the series?

• a_n = 5n + 2

• a_n = 2n + 5

• a_n = 7n + 5

• a_n = 5n - 2

What is the value of n that generates the last term in the series?

• 11

• 12

• 10

• 13

What is the last term in the series?

• 66

• 62

• 64

• 60

What is the first step in solving for n in the equation 2 + 5n = 62?

• Add 2 to both sides

• Multiply both sides by 5

• Subtract 2 from both sides

• Divide both sides by 5

How do you calculate the sum of the series?

• Multiply the first term by the number of terms

• Use the formula S_n = n/2 * (a_1 + a_n)

• Add all terms manually

• Use the formula S_n = n * (a_1 + a_n)

What is the sum of the series?

• 400

• 412

• 414

• 416

What is the value of S_12 in the series?

• 414

• 420

• 440

• 430

What is the formula for the sum of an arithmetic series?

• S_n = n/2 * (a_1 + a_n)

• S_n = n * (a_1 - a_n)

• S_n = n * (a_1 + a_n)

• S_n = n/2 * (a_1 - a_n)