Analyzing Sequences and Formulas

The video tutorial explains how to use polynomial fitting to find the formula for the nth term of a sequence. It begins by determining if the sequence is delta k constant, then derives the closed formula using first and second differences. The tutorial demonstrates solving a system of equations to find the coefficients of the polynomial, specifically using the elimination method. The final closed formula is presented as a degree two polynomial.

What is the purpose of using polynomial fitting in sequence analysis?

• To calculate the average of the sequence

• To find the sum of the sequence

• To determine the nth term formula

• To identify the maximum value in the sequence

What does it mean for a sequence to be delta k constant?

• The sequence has a constant sum

• The sequence has a constant average

• The sequence has a constant product

• The kth sequence of differences is constant

What is the first difference of the sequence 1, 2, 8, 19, 35?

• 3, 7, 13, 21

• 1, 4, 9, 16

• 1, 6, 11, 16

• 2, 6, 12, 20

Why is the sequence of first differences considered arithmetic?

• The terms are decreasing by 5

• The terms are constant

• The terms are random

• The terms are increasing by 5

What form does the closed formula take for a delta 2 constant sequence?

• a n + b

• a n^4 + b n^3 + c n^2 + d n + e

• a n^2 + b n + c

• a n^3 + b n^2 + c n + d

What is the value of c in the closed formula for the sequence?

• 3

• 2

• 1

• 0

Which method is used to solve the system of equations for a and b?

• Substitution

• Graphing

• Matrix inversion

• Elimination

What is the value of a in the closed formula?

• 5/2

• 9/2

• 7/2

• 3/2

What is the value of b in the closed formula?

• -7/2

• -5/2

• -1/2

• -3/2

What is the final closed formula for the sequence 1, 2, 8, 19, 35?

• 5/2 n^2 + 3/2 n + 1

• 5/2 n^2 - 3/2 n + 1

• 3/2 n^2 - 5/2 n + 1

• 3/2 n^2 + 5/2 n + 1