Arithmetic Sequences
Lesson Objectives:
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You should be able to identify if a sequence is arithmetic
Given an arithmetic sequence, you should be able to determine “a” and “d’.
You should be able to determine the “nth term” of an arithmetic sequence
You should be able to apply the “nth term” formula to various problem solving situations
A) Definition of an Arithmetic Sequence
You have just classified many different sequences. Select two from the group we called arithmetic.
Sequence
Calculations
U2 – U1 =
U3 – U2 =
U4 – U3 =
U5 – U4 =
Un – Un-1 =
U2 – U1 =
U3 – U2 =
U4 – U3 =
U5 – U4 =
Un – Un-1 =
U2 – U1 =
U3 – U2 =
U4 – U3 =
U5 – U4 =
Un – Un-1 =
An ARITHMETIC SEQUENCE is a sequence of numbers…
What do I see?
Arithmetic Sequences
B) The General Term of Nth Term of an Arithmetic Sequence
Consider the arithmetic sequence
Position
of term
“n”
Term Un
1
2
3
4
a
a+d
a + 2d
a + 3d
5…..
The General term (nth Term) of an Arithmetic Sequence is:
Un = ____________
10…..
84…..
n
What does the nth term mean?
where n is _______________
a is _____________
What can we use it for?
d is _____________
C) Using the nth Term – In your home groups of 4, select a number 1-4.
Problem 1
Problem 2
Is this sequence arithmetic? Justify your answer.
For the arithmetic sequence: 135, 118, 101, 84,….
-9.4, -3.3, -1.6, 0.1,……
Determine a and d, and hence an equation for Un
Determine the equation of the nth term.
Problem 3
Problem 4
Determine the first 5 terms of the sequence:
For the arithmetic sequence: 13, 19, 25, 31, 37,….
Un = 18 – 2.5n
Determine U25
Arithmetic Sequences
D) Practice
OXFORD Unit.pdf - Exercise 7A Exam Style Questions
Cirrito unit.pdf – Exercise 12.1.1 Questions 3, 4, 6, 9
Haese and Harris - Math Studies – Exercise 12 C page 402
E) Challenge - Use your understanding of nth term to help with these problems.
1.
Is the term -916 a term in the sequence Un = 120 – 14n
2. For a given arithmetic sequence, a = 2, and U65 = 327, figure out U14
3. For a given arithmetic sequence, U4 = 74, and U18 = 18,, figure out the equation of Un