
Understanding Sequences and Recurrence Relations

Interactive Video
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Mathematics
•
9th - 12th Grade
•
Hard

Aiden Montgomery
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial sequence given in the problem?
1, 3, 6, 10, 15, 21
2, 4, 8, 16, 32, 64
5, 10, 20, 40, 80, 160
3, 5, 11, 21, 43, 85
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the term a sub 6 calculated?
By adding 2 times the previous term to the current term
By adding 2 times the term before the previous term to the previous term
By multiplying the previous term by 2
By subtracting the previous term from the current term
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the recursive formula for the sequence?
a sub n = 2 * a sub n-1 + a sub n-2
a sub n = a sub n-1 + 2 * a sub n-2
a sub n = a sub n-1 + a sub n-2
a sub n = a sub n-1 - 2 * a sub n-2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the initial conditions required for the recursive definition?
a sub 0 = 5, a sub 1 = 10
a sub 0 = 3, a sub 1 = 5
a sub 0 = 1, a sub 1 = 2
a sub 0 = 2, a sub 1 = 4
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the characteristic equation derived from the recurrence relation?
x^2 + x + 2 = 0
x^2 - x - 2 = 0
x^2 - 2x + 1 = 0
x^2 + 2x - 1 = 0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the roots of the characteristic equation?
x = 1 and x = -2
x = 0 and x = 3
x = 2 and x = -1
x = -1 and x = 1
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the form of the solution to the recurrence relation?
a sub n = a * n^2 + b * n
a sub n = a * 2^n + b * (-1)^n
a sub n = a * 3^n + b * 2^n
a sub n = a * n + b * n^2
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