Arithmetic Series and Sequences

The video tutorial explains how to find the sum of an arithmetic sequence starting from 3 and ending at 723. It covers identifying the sequence, calculating the number of terms, and using a specific technique to find the sum. The sequence has a common difference of 6, and the sum is calculated to be 43,923.

What is the common difference in the arithmetic sequence discussed?

• 3

• 6

• 9

• 12

How do you find the common difference in an arithmetic sequence?

• By dividing the sum by the number of terms

• By subtracting the first term from the last term

• By subtracting any term from the next term

• By adding the first and last terms

What is the closed formula for the sequence given the first term is 3 and the common difference is 6?

• a_n = 3 + 6n

• a_n = 6 + 3n

• a_n = 3n + 6

• a_n = 6n + 3

How many terms are there in the sequence from 3 to 723?

• 120

• 122

• 121

• 123

What is the first step in finding the sum of the arithmetic series using the discussed technique?

• Write the series in reverse order

• Subtract the first term from the last term

• Add all terms directly

• Multiply the first and last terms

When the series is written in reverse order, what is the sum of each pair of terms?

• 726

• 723

• 717

• 720

How many pairs of terms are summed to find the total sum of the series?

• 61

• 120

• 121

• 60

What is the final sum of the arithmetic series from 3 to 723?

• 43,923

• 43,000

• 87,846

• 44,000

What operation is performed after finding the sum of all pairs to get the final sum?

• Divide by 2

• Multiply by 2

• Subtract 2

• Add 2

What is the significance of the number 726 in the calculation of the sum?

• It is the last term of the series

• It is the sum of each pair of terms

• It is the first term of the series

• It is the common difference