Recursive and Closed Form Sequences

The video tutorial explains an arithmetic sequence starting with 5 and having a common difference of 3. It covers the recursive definition, deriving the closed formula, verifying if a number is a term in the sequence, and counting the total number of terms. The tutorial provides step-by-step calculations and explanations to help understand these concepts.

What is the first term of the sequence discussed in the video?

• 11

• 3

• 5

• 8

What is the common difference in the sequence?

• 4

• 3

• 2

• 5

Which of the following is the correct recursive formula for the sequence?

• a_n = a_(n-1) + 2

• a_n = a_(n-1) + 3

• a_n = a_(n-1) + 4

• a_n = a_(n-1) + 5

What is the closed formula for the nth term of the sequence?

• a_n = 3 + 5n

• a_n = 5 + 3n

• a_n = 3 + 2n

• a_n = 2 + 3n

If n equals 1, what is the value of a_n according to the closed formula?

• 2

• 3

• 5

• 8

Is 2627 a term in the sequence?

• Yes, it is the 800th term

• Yes, it is the 875th term

• No, it is the 900th term

• No, it is not a term

What is the value of n if 2627 is a term in the sequence?

• 900

• 875

• 850

• 800

How many terms are there in the sequence up to 1568?

• 500

• 575

• 522

• 550

What is the last term of the sequence if it has 522 terms?

• 1570

• 1560

• 1565

• 1568

What is the formula used to find the number of terms in the sequence?

• a_n = a_1 + d(n-1)

• a_n = a_0 + d(n-1)

• a_n = a_1 + d(n)

• a_n = a_0 + d(n)