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
12.)
1, 4, 7, 10, 13, 16, ...
What is the slope (m)?
What is the common
difference (d)?
What is the y-intercept?
What is a 0 ?
Arithmetic Sequences
defined recursively
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.
15.)
4, 7, 10, 13, 16, 19, 22, ...
a1 =
What is the explicit
equation? y  mx  b
What is the explicit
equation? a n  dn  a0
an = an-1 +
16.)
54, 56, 58, 60, 62, 64, …
a1 =
13.) 5, 15, 25, 35, 45, ...
What is the slope (m)?
What is the common
difference (d)?
What is the y-intercept?
What is a 0 ?
an = an-1
17.)
90, 85, 80, 75, 70, 65,…
a1 =
What is the explicit
equation? y  mx  b
What is the explicit
equation? a n  dn  a0
an =
18.)
-7, -5, -3, -1, 1, 3, 5,…
19.)
12, 7, 2, -3, -8, -13,…
14.) 11, 6, 1, -4, -9, ...
What is the slope (m)?
What is the common
difference (d)?
What is the y-intercept?
What is a 0 ?
What is the explicit
equation? y  mx  b
What is the explicit
equation? a n  dn  a0
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.) 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:
5.) 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:
Make up your own arithmetic sequence and do your own problem
6.)
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.
7.) a1  4
9.) an  2n  1
an  an1  3
8.) a1  10
10.) an  3n
an  an1  2
11.) Here’s how many push-ups Tony
did per day. The pattern continued.
Recursive: _____________________________
Recursive: _____________________________
Explicit: ____________________________
Explicit: ____________________________