Arithmetic Sequences and Their Sums

The video tutorial explains how to define an arithmetic sequence recursively, with each term being 11 more than the previous one, starting from 4. The challenge is to find the sum of the first 650 terms. The video walks through the formula for the sum of an arithmetic series and calculates the 650th term. Finally, it demonstrates the complete calculation of the sum using a calculator.

What is the base case for the arithmetic sequence defined in the video?

• The first term is 11

• The first term is 4

• The first term is 0

• The first term is 650

What is the common difference in the arithmetic sequence?

• 11

• 7143

• 650

• 4

What is the challenge presented in the video regarding the arithmetic sequence?

• Find the sum of the first 100 terms

• Find the 100th term

• Find the sum of the first 650 terms

• Find the 650th term

Which formula is used to find the sum of an arithmetic sequence?

• Sum of all terms divided by the number of terms

• First term plus last term divided by two, times the number of terms

• Last term minus first term

• First term times the number of terms

How is the 650th term of the sequence calculated?

• By adding 11 to the first term 650 times

• By subtracting 11 from the first term 649 times

• By adding 11 to the first term 649 times

• By multiplying the first term by 650

What is the value of the 650th term in the sequence?

• 4

• 650

• 11

• 7143

How many times is 11 added to reach the 650th term?

• 651 times

• 649 times

• 650 times

• 648 times

What is the final step in calculating the sum of the first 650 terms?

• Multiply the average of the first and last terms by 650

• Add the first and last terms

• Divide the sum of the first and last terms by 650

• Subtract the first term from the last term

What is the sum of the first 650 terms of the sequence?

• 2,322,775

• 11

• 7143

• 650

What is the average of the first and last terms used in the sum formula?

• 7143

• 650

• 3573.5

• 4