3536SequencesPatterns Flashcards
What is a sequence?
Given a sequence of numbers, what is the model that produced them?
What is this concept in calculus?
Infinite series
Find the formula for the nth term in:
1, 3, 5, 7, ….
2n - 1 = nth term
Where n is the position of the term.
The second term is
(2*2) - 1
What is the formula for the nth term:
1, ½, ⅓, ¼ …
The first term is 1/1, the second is ½.
:: 1/n where n is the position
Find the formula for the nth term:
3, 7, 27, 81 …
The first term is 31.
The second term is 3².
:: 3n
Find the formula for the nth term:
2, 10, 50, 250 1250 …
The first term is 2.
The second term is 2*5(n-1).
The third term is 2*5(n-1)
:: 2*5(n - 1)
where n is the position
What is a geometric sequence?
Each number is multiplied by a constant.
What is the formula for:
2, -4, 8, -18, 32 …
The first term is 2.
The second term is -(-2n) = -4
The third term is -(-2n) = 8
:: - (-2n)
What is an arithmetic sequence?
One term is built on another by addition.
What model creates the sequence:
2, 5, 8, 11, 14, 17 …
The first term is 2.
The second term is 2 + (n-1)*3
where n is the position.
2 + (2-1)*3 = 5
:: 2 + (n-1)*3
What model creates the sequence:
5, 12, 19, 26, 33, 40 …
The first term is 5.
The second term is 5 + 7*(n - 1)
The third term is 5 + 7*(n - 1)
:: 5 + 7*(n - 1)
What is a quadratic sequence?
A sequence whose model is in the form:
an² + bn + c
What is the sequence that produces:
3, 6, 11, …
an² + bn + c
The 1st term is 1a + 1b + c = 3
The 2nd term is 4a + 2b + c = 6
The 3rd term is 9a + 3b + c = 11
Subtract 1 from 2: 3a + b = 3 ::b = 3 - 3a
Subtract 2 from 3: 5a + b = 5
5a + (3 - 3a) = 5
2a = 2 ::a = 1
:: b = 0
:: c = 2
n² + 2
What type of model produces:
2, 18, 52, 110, 198, 322 …
It takes more than 2 steps to get to the next number, so it was created by a cubic polynomial.
How can you determine if it is a cubic trinomial sequence?
Layout the terms and see how many steps it takes to get to the same number.
