Understanding Sequences and Formulas

The video tutorial explains how to determine the first five terms of a sequence defined by a_n = n^2 - 3n + 1. It then explores methods to find a closed formula for a different sequence starting with 3, 10, 21, 36, 55, and so on. The tutorial demonstrates that the sequence can be expressed as the sum of n(n+1) and n^2, leading to a closed formula of 2n^2 + n. The video concludes with a simplification and factorization of the formula.

What is the formula for the sequence a_n?

• n^2 + n - 3

• n^2 - n + 3

• n^2 - 3n + 1

• n^2 + 3n + 1

What is the value of a_3 in the sequence a_n = n^2 - 3n + 1?

• 5

• 11

• 1

• -1

What is the value of a_5 in the sequence a_n = n^2 - 3n + 1?

• 11

• 5

• 21

• 15

Which of the following is the correct sequence of the first five terms of a_n = n^2 - 3n + 1?

• -1, -1, 1, 5, 11

• 1, -1, 1, 5, 11

• -1, 1, -1, 5, 11

• 1, 1, 1, 5, 11

What is the first term of the new sequence starting with 3, 10, 21, 36, 55?

• 3

• 10

• 36

• 21

What is the difference between the first and second terms of the sequence 3, 10, 21, 36, 55?

• 8

• 7

• 6

• 5

Which two sequences are summed to find the closed formula for the new sequence?

• n^2 and n(n+1)

• n(n+1) and n(n+1)

• n^2 and n(n-1)

• n^2 and n^2

What is the closed formula derived for the sequence starting with 3, 10, 21, 36, 55?

• 2n^2 + n

• n^2 + n

• n^2 - n

• 2n^2 - n

What is the simplified form of the closed formula 2n^2 + n?

• n(2n + 1)

• n(2n - 1)

• 2n(n + 1)

• 2n(n - 1)

What is the greatest common factor used to factor the expression 2n^2 + n?

• 2

• n

• 1

• n^2