Arithmetic Sequences and Their Properties

The video tutorial explains how to work with an arithmetic sequence, starting with identifying the common difference and deriving the closed formula. It then demonstrates how to calculate the sum of the sequence using a specific technique. The tutorial also explores a related sequence, b sub n, and shows how it is connected to the original sequence through partial sums.

What is the common difference in the arithmetic sequence discussed?

• 8

• 5

• 3

• 2

How do you find the closed formula for an arithmetic sequence?

• By adding the first term to the common difference

• By subtracting the common difference from the first term

• By multiplying the first term by the common difference

• By adding the first term to the product of the common difference and (n-1)

What is the value of n when the nth term of the sequence is 1463?

• 450

• 500

• 400

• 487

What is the sum of the arithmetic sequence with 487 terms?

• 350,000

• 357,458

• 300,000

• 400,000

What is the last term in the arithmetic sequence before 1463?

• 1459

• 1458

• 1461

• 1460

How many terms are there in the sum of the arithmetic sequence?

• 400

• 450

• 500

• 487

What is b sub zero in the new sequence?

• 6

• 5

• 0

• 1

How is b sub one calculated in the new sequence?

• By dividing a sub one by 1

• By multiplying 1 with a sub one

• By subtracting 1 from a sub one

• By adding 1 to a sub one

What is the relationship between b sub n and the arithmetic sequence?

• b sub n is the product of the arithmetic sequence

• b sub n is one plus the partial sums of the arithmetic sequence

• b sub n is the sum of the arithmetic sequence

• b sub n is the difference of the arithmetic sequence

What is the closed formula for b sub n?

• b sub n = 1 + n/2 * (7 + 3n)

• b sub n = 1 + n * (7 + 3n)

• b sub n = 1 + n/2 * (5 + 3n)

• b sub n = 1 + n * (5 + 3n)