Download Sequences As Functions

Arithmetic Sequences
Name_____________________________
Arithmetic Sequences – we add/subtract to get the
next value.
1.) Given the arithmetic sequence, write down what
the common difference (d) is.
a.) 1, 4, 7, 10, 13, 16, ...
d=
b.) 8, 18, 28, 38, 48, ...
d=
c.) 10, 5, 0, -5, -10, ...
d=
1
1
d.) 1,
, 0,  , ...
2
2
d=
5.) Find the 15th number in this sequence:
1, 4, 7, 10, 13, 16, ...
6.) Find the 11th number in this sequence:
8, 18, 28, 38, 48, ...
7.) Find the 6th number in this sequence:
10, 5, 0, -5, -10, ...
a7  that 7 is called a subscript
a7 is pronounced “a sub 7”
8.) Find the 52nd number in this sequence:
3, 7, 11, 15, 19, 23, …
2.) Fill in the blanks for the sequence
3, 6, 9, 12, 15, 18, 21, 24, 27…
a1= ____, a4 = ____, a9 = ____,…
a100=______
(bonus)
3.) Fill in the blanks for the sequence
Sequences are functions that have the natural
numbers as their domain.
9a.) What are the natural numbers?
-5, -1, 3, 7, 11, 15, 19, …
when n = 1, an = ______________
b.) What would this sequence look like as a table?
100, 200, 300, 400, 500, …
when n = 2, an = ______________
when n = 5, an = ______________
4.) Fill in the blanks for the sequence
10.) Write the first five numbers in the sequence:
a n  2n  1 (which is the same as y = 2x + 1)
8, 18, 28, 38, 48, 58, 68, …
when n = 5, an = ______________
a1= ____, a2 = ____, a3 = ____, a4= ____, a5 = ____
an+1 = ______________
an+2 = ______________
an-1 = ______________
an-2 = ______________
11.) Write the first five numbers in the sequence:
a1  5 and
an  an1  3
(Recursive!)
a1= ____, a2 = ____, a3 = ____, a4= ____, a5 = ____
Arithmetic Sequences
defined explicitly
Arithmetic Sequences
defined recursively
What is the common
difference (d)?
What is the slope (m)?
To define a function recursively:
1.) always give people the 1st term (a1)
2.) Tell people what to do to get the next
number using the previous number.
What is a 0 ?
What is the yintercept?
15.)
12.)
1, 4, 7, 10, 13, 16, ...
4, 7, 10, 13, 16, 19, 22, ...
a1 =
What is the explicit
equation? a n  dn  a0
an = an-1 +
What is the explicit
equation?
y  mx  b
16.)
54, 56, 58, 60, 62, 64, …
a1 =
13.) 5, 15, 25, 35, 45, ...
What is the common
difference (d)?
What is the slope (m)?
What is a 0 ?
What is the yintercept?
an = an-1
17.)
90, 85, 80, 75, 70, 65,…
a1 =
What is the explicit
equation?
a n  dn  a0
an =
What is the explicit
equation? y  mx  b
18.)
-7, -5, -3, -1, 1, 3, 5,…
19.)
12, 7, 2, -3, -8, -13,…
14.) 11, 6, 1, -4, -9, ...
What is the common
difference (d)?
What is the slope (m)?
What is a 0 ?
What is the y-intercept?
What is the explicit
equation? a n  dn  a0
What is the explicit
equation? y  mx  b
20.) 16, 18, 20, 22, 24, 26,…
Recursive and Explicit
1.) -1, -2, -3, -4, -5, -6, -7, …
a64 =
a.) Write the explicit equation that represents the
sequence:
b.) Write the recursive equation that represents the
sequence:
2.) 3, 4, 5, 6, 7, 8, 9, ...
a64 =
a.) Write the explicit equation that represents the
sequence:
b.) Write the recursive equation that represents the
sequence:
3.) 2, 4, 6, 8, 10, 12, ...
a64 =
a.) Write the explicit equation that represents the
sequence:
b.) Write the recursive equation that represents the
sequence:
4.) 5, 7, 9, 11, 13, 15, 17…
a64 =
a.) Write the explicit equation that represents the
sequence:
b.) Write the recursive equation that represents the
sequence:
Given the recursive definition, write
the explicit definition.
Given the explicit definition, write the
recursive definition.
5.) a1  4
6.) an  2n  1
an  an1  3
7.) a1  10
an  an1  2
8.) an  3n
9.) Here’s how many push-ups Tony did
per day. The pattern continued.
Recursive: _____________________________
Recursive: _____________________________
Explicit: ____________________________
Explicit: ____________________________