Download LEARNING GOAL: To Examine and Use Arithmetic Sequences

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Algebra 2/Trig – Arithmetic Sequences CLASSWORK
DATE:_________
PERIOD:_______
LEARNING GOAL: To Examine and Use Arithmetic Sequences
Sequence Definitions

A sequence is an ordered list of numbers. ex: 1, 4, 7, 10, 13

The sum of the terms in a sequence is called a series. ex: 1 + 4 + 7 + 10 + 13

Each number of a sequence is called a term.

A finite sequence contains a finite number of terms (you can count them). ex: 1, 4, 7, 10, 13

An infinite sequence contains an infinite number of terms (you cannot count them). ex: 1, 4, 7, 10, 13, ….

The terms of a sequence are referred to in the subscripted form shown below, where the subscript refers to
the location (position) of the term in the sequence.
MODEL PROBLEMS WITH SEQUENCES
**TO FIND A SPECIFIC TERM WHEN GIVEN THE FORMULA, JUST SUBSTITUTE THE NUMBER OF THE TERM YOU
WANT TO FIND**
1. Write the first two terms of the sequence whose nth
term is given by the explicit formula:
2. Find the 7th term of the sequence whose nth term is
( ) (
)
given by:
Arithmetic Sequences

If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred
to as an arithmetic sequence. The number added to each term is constant (always the same).

The fixed amount is called the common difference, d, referring to the fact that the difference between two
successive terms yields the constant value that was added.

To find the common difference, subtract the first term from the second term.
Examples: Find the common difference (d) of each arithmetic sequence
a. 1, 4, 7, 10, 13, 16, ...
b. 15, 10, 5, 0, -5, -10, ...
c. n +1, n +5, n +9, n +13, ...
Arithmetic Sequence Formula (Rule) – MEMORIZE!!!!

To find any term of an arithmetic sequence use the formula
(
)
where a1 is the first term of the sequence, d is the common difference, n is the number of the term to find.
Model 1: What is a formula for the nth term of sequence 3, 5, 7, 9, ...

Why is this an arithmetic sequence?
Model 2: Write a rule for the nth term of sequence 57, 45, 33, 21, ...
Then use this formula to find the fifteenth term of the sequence.

Why is this an arithmetic sequence?
Model 3: Find the common difference if the first term is 6 and the twentieth term is 82.

Why is this an arithmetic sequence?
More Difficult Arithmetic Sequence Questions

How can you find the common difference of an arithmetic sequence if you are given 2 terms that are not
consecutive?
MODEL 1: The fifth term of an arithmetic sequence is 26 and the eighth term is 41. What is the common
difference of this sequence?
MODEL 2: If the 20th term of an arithmetic sequence is 100 and the 40th term of the sequence is 250, what is the
first term of the sequence?
CLASSWORK
1. What is the common difference of the arithmetic sequence {2n – 3, 3n – 5, 4n – 7, 5n – 9}?
2. Write a rule for the nth term of sequence 2, -1, -4, -7, …
3. Find the 25th term of the sequence -7, -4, -1, 2, ...
4. In an arithmetic sequence,
and
. Determine a formula for
, the
term of this sequence.