Algebra 1 : How to find the nth term of an arithmetic sequence
Study concepts, example questions & explanations for Algebra 1
All Algebra 1 Resources
Example Questions
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
The first term of an arithmetic sequence is 
To find the common difference 
For us, 
Now we can solve for 
Add the common difference to the first term to get the second term.
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
The sum of the first three terms of an arithmetic sequence is 111 and the fourth term is 49. What is the first term?
It cannot be determined from the information given.
Let 
The sum of the first three terms is 
Now we know that the second term is 37. The fourth term is the second term plus twice the common difference: 
The common difference is 6. The first term is 
Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence
An arithmetic sequence begins with 
For arithmetic sequences, we use the formula d "a_{n} = a_{1}+(n-1)d")
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
The fourth and tenth terms of an arithmetic sequence are 372 and 888, respectively. What is the first term?
Let 
Example Question #3 : How To Find The Nth Term Of An Arithmetic Sequence
The ninth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?
The common difference of the sequence is the difference of the tenth and ninth terms: 
The ninth term of an arithmetic sequence with first term 
Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence
The eighth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?
The eighth and tenth terms of the sequence are 
Now set eighth term 
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, . . .
53
41
37
45
49
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
All Algebra 1 Resources
