Download A sequence is a list of ordered elements. Example: { 1, 2, 4, 8, 16

Aim #85: How do we identify number sequences?
Homework: Handout
Do Now: Find the next term in the following number patterns.
1, 5, 9, 13, ______
4-6-17
-4, 8, -16, 32, ________
A sequence is a list of ordered elements.
Example: { 1, 2, 4, 8, 16, ...}
Each term in the sequence is indexed. {a 1, a2, a3, a4, a5, ...}. In the example a3 = 4.
n-1
Do you agree that this sequence can be identified as an = 2
if n ≥ 1 ?
In general, a sequence is defined by a function f from a domain of natural numbers
to a range of real numbers that satisfy the equation f(n) = an.
Example: f(n) = 2n + 1
If domain is {1,2,3,4,...}, what is the range?
1) Write the sequence from the given explicit formula:
n
f(n) = 3 - 4 for n ≥ 1.
2) a) Find the next term in the sequence { 3, 6, 9, 12, ... }. ________
th
b) Is it possible to find the 25 term in this sequence without writing out the
sequence?
c) Write a formula using either function notation or an notation to determine the
th
n term of the sequence (write an equation that will find any n value).
th
3) Examine the two sequence formulas:
n
n-1
f(n) = 3 for {n Whole or n ≥ 0} and f(n) = 3
for {n Natural or n ≥ 1}
Mathematically, there is no difference between the formulas. We will use the
domain {n Natural}. It keeps a1 = f(1).
Term #
1
2
3
4
5
6
7
Term
1
2
4
8
16
32
64
f(4) = a4 = 8
5) Write the explicit formula for the sequence above in function notation.Be sure to
specify what value of n your formula starts with.
6) Consider the sequence that follows a "plus 3" pattern: {4, 7, 10, 13, 16, ...}
a) Write the formula for the sequence in an form. ______________________
b) Graph the terms of the sequence as ordered pairs ( n, an ) on the coordinate plane.
an
What do you notice about all the points?
n
7) Consider a sequence that follows a "minus 5" pattern: {30, 25, 20, 15, ...}
th
a) Write the formula for the n term of the sequence. Be sure to specify what
value of n your formula starts with.
th
b) Using the formula, find the 20 term.
8) Consider the sequence that follows a "times 5" pattern: {1, 5, 25, 125, ...}
th
a) Write a formula for the n term of the sequence. Be sure to specify what value
of n your formula starts with.
b) Using the formula, find the 10th term.
c) Graph the terms of the sequence as ordered pairs ( n, f(n)) on the coordinate
plane.
f(n)
n
9) A standard letter-sized piece of paper is 8.5 by 11 inches.
a) Find the area of one piece of paper.
b) If the paper were folded completely in half, what would be the area ofthe
resulting rectangle.
c) Write the formula for a sequence to determine the area of the paper after n
folds.
d) What would the area be after 7 folds?
10) Consider the sequence formed by the square numbers:
th
a) Write a formula for the n term of the sequence. Be sure to specify what value of
n your formula starts with.
f(n)
th
b) Using the formula, find the 50 term.
c) Graph the terms of the sequence as
ordered pairs (n, f(n)) on the
coordinate plane.
n
Let's sum it up!
A sequence can be thought of as an ordered list of elements. To define the pattern
of a sequence, an explicit formula is often given, and unless specified otherwise,
the first term is found by substituting one into the formula.