Download GUIDED NOTES – Lesson 8-1

GUIDED NOTES – Lesson 8-1
Sequences
Name: ______________________ Period: ___
STANDARD: (F-BF.2) Write arithmetic and geometric sequences both recursively and with an explicit formula,
use them to model situations, and translate between the two forms.
OBJECTIVES: I can...
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Determine the explicit formula for a given sequence.
Generate terms in sequence, given the explicit formula.
Identify the pattern of a sequence and generate additional terms.
Apply sequences to real-life scenarios and problems.
A sequence is an ordered list of numbers.
Each number is considered a _________ within the sequence.
2, 5, 8, 11, 14, 17, …
These terms are referred to in subscripted form as ______.
Each subscript refers to the ____________ of a number in the sequence.
That is a2 in the sequence above?
a7?
A
10?
When sequences have a definite pattern in a given sequence, we are able to figure out what
we call the sequence’s ___________ formula.
2, 5, 8, 11, 14, 17, …
It IS increasing by _____, but the formula has to relate to the position of the numbers.
an
2
5
8
11
14
17
n
1
2
3
4
5
6
Sometimes the explicit formula is hard to see initially.
When given choices, you might have to test each formula
out until you find one that works.
What has to be done to every n value for it to generate the an term?
You need to be able to generate the terms in a sequence given the explicit formula. You do
this by plugging in the term to find the resulting number.
A) an = n + 3
B) an = 2n
C) an = 3n + 1
D) an = n2 + 1
E) an = 3n – 1
Examples:
A) Write the first three terms of the sequence whose nth term is given by the explicit formula:
an = 2n + 1
(First three means plug in…
B) Find the 5th and 16th terms in the sequence whose nth term is given by the explicit formula:
an = -n – 3
(We only need to plug in ____ and ____)
In the next example, you need to keep the sequence going until you hit the terms requested.
C) Find the 8th and 11th terms in the following sequence.
5, 9, 13, 17, …
D) Find the 5th and 12th terms of the sequence whose nth term is given by:
an 
n
n2
E) Find the first 4 terms of the sequence:
an  (1) n (n  3)
F) Abe agreed to work for his brother at a construction job for one dollar per hour, if his pay
was doubled every three hours.
an  1, 1, 1, 2, 2, 2, 4, 4, 4, 8, …
How much was he getting paid on the 17th hour of work?
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