Lesson 5-A Notes(3-5)
Arithmetic Sequences
TNSS F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.
TNSS A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
Past Target
I identified linear functions.
Present Target
I can recognize arithmetic
sequences.
Future Target
I will work with geometric
sequences.
I can find the next term of an
arithmetic sequence.
I can write an equation to find the
nth term of an arithmetic
sequence.
An ________________________________________________________________ is a numerical pattern that
increases or decreases at a constant rate called the________________________________________________.
Ex. 1 Determine whether each sequence is an arithmetic sequence. Write yes or no. If yes, state the
common difference.
a. -15,-13,-11,-9,...
b.
7 5 1 5
, , , - ,...
8 8 8 8
Ex. 2 Find the next three terms of each arithmetic sequence.
a. -8,-11,-14,-17,...
b. 1.5,3, 4.5, 6,...
The nth term an of an arithmetic sequence with first term ________________ and common
difference______________
is given by _________________________________________ ,where
_____________ is a positive integer.
Ex. 3 - Write an equation for the nth term of the arithmetic sequence. Then graph the first five terms.
a. 30, 26, 22, 18, ….
b. -7, -4, -1, 2, …
Ex. 4 Using the arithmetic sequence 7, 11, 15, 19, …
A) Write an equation for the nth term of the arithmetic sequence.
B) Find the 65th term of the sequence.
C) Which term of the sequence is 411?
REAL-WORLD EXAMPLE---EXERCISE
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests jogging for 12
minutes each day for the first week. Each week thereafter, he suggests that you increase that time by 6
minutes.
A) How many minutes will you
be jogging per day the 8th week?
B) How many weeks will it be before you are
jogging 60 minutes per day?
YOU TRY:
Determine whether each sequence is an
arithmetic sequence.
Write yes or no.
If yes, state the common difference.
1) -26, -22, -18, -14, …
2) 1, 4, 9, 25, …
YOU TRY:
Find the next three terms of each
arithmetic sequence.
1) 29, 35, 41, 47, …
2) -4, -8, -12, -16, …
YOU TRY:
Write an equation for the nth term of
the arithmetic sequence. Then graph
the first five terms.
7, 13, 19, 25, ….
YOU TRY:
Using the arithmetic sequence
19, 31, 43, 55, …
A) Write an equation for the nth term of
the arithmetic sequence.
B) Find the 50th term of the sequence.
C) Which term of the sequence is 967?