Algebra 1 : Functions and Lines
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Example Questions
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
Find the 100th term in the following arithmetic sequence
Before we can figure out the 100th term, we need to find a rule for this arithmetic sequence. Remember, the general rule for this sequence is
where 
In our problem, 
Now that we found our rule, we can go on and figure out what the 100th term is equal to. For the 100th term, 
Example Question #8 : How To Find The Nth Term Of An Arithmetic Sequence
To find any term of an arithmetic sequence:
Where 
Find the 18th term of the following arithmetic sequence.
Start by finding the common difference, 
Then, using the formula given before the question:
Example Question #9 : How To Find The Nth Term Of An Arithmetic Sequence
To find any term of an arithmetic sequence:
Where 
Find the 26th term of the following arithmetic sequence.
Start by finding the common difference in terms by subtracting the first term from the second.
Then, fill in the rest of the equation given before the question.
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
Given the the sequence below, what is the 11th term of the sequence?
1, 5, 9, 13, . . .
45
49
53
41
37
41
The 11th term means there are 10 gaps in between the first term and the 11th term. Each gap has a difference of +4, so the 11th term would be given by 10 * 4 + 1 = 41.
The first term is 1.
Each term after increases by +4.
The nth term will be equal to 1 + (n – 1)(4).
The 11th term will be 1 + (11 – 1)(4)
1 + (10)(4) = 1 + (40) = 41
Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence
The second term of an arithmetic sequence is 
The common difference between the terms is half that between the second and fourth terms - that is:
Subtract this common difference from the second term to get the first:
Example Question #12 : How To Find The Nth Term Of An Arithmetic Sequence
An arithmetic sequence is given by the formula 
You can either calculate the vaules of 
Example Question #11 : Arithmetic Series
Consider the following arithmetic sequence:
What is the 
A simple way to find the 
Here, 
Example Question #14 : How To Find The Nth Term Of An Arithmetic Sequence
What is the 20th term of 
Notice that every odd term is increasing at an increment of 
The even terms are 
The equation that represents the terms for this sequence is: 
Substitute 
The answer is:
Example Question #31 : Sequences
What is the 11th term in the following sequence?
First we need to show how this sequence is changing. Let's call the first number
Ok, so we have established that the sequence is shrinking by 9 each time. So now we need to calculate out to the 11th term. Starting from the first term, we need to subtract 9 ten times to get to the 11th term. So that would look like this.
Example Question #11 : Arithmetic Series
Which of the following is an example of an arithmetic sequence?
Each of these sequences is an arithmetic sequence.
Each of these sequences is an arithmetic sequence.
In each case, the terms increase by the same number, so all of these sequences are arithmetic.
Each term is the result of adding 1 to the previous term. 1 is the common difference.
Each term is the result of subtracting 1 from - or, equivalently, adding 
The common difference is 0 in a constant sequence such as this.
Each term is the result of adding 
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