How to find the next term in an arithmetic sequence - Algebra 1
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In the following arithmetic sequence, what is 
?
In the following arithmetic sequence, what is
The question states that the sequence is arithmetic, which means we find the next number in the sequence by adding (or subtracting) a constant term. We know two of the values, separated by one unknown value.
We know that 
is equally far from -1 and from 13; therefore 
is equal to half the distance between these two values. The distance between them can be found by adding the absolute values.
The constant in the sequence is 7. From there we can go forward or backward to find out that 
.
The question states that the sequence is arithmetic, which means we find the next number in the sequence by adding (or subtracting) a constant term. We know two of the values, separated by one unknown value.
We know that
The constant in the sequence is 7. From there we can go forward or backward to find out that
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Given the sequence below, what is the sum of the next three numbers in the sequence?
Given the sequence below, what is the sum of the next three numbers in the sequence?
By taking the difference between two adjacent numbers in the sequence, we can see that the common difference increases by one each time.
Our next term will fit the equation 
, meaning that the next term must be 
.
After 
, the next term will be 
, meaning that the next term must be 
.
Finally, after 
, the next term will be 
, meaning that the next term must be 
The question asks for the sum of the next three terms, so now we need to add them together.
By taking the difference between two adjacent numbers in the sequence, we can see that the common difference increases by one each time.
Our next term will fit the equation
After
Finally, after
The question asks for the sum of the next three terms, so now we need to add them together.
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Find the next term in the following sequence.
Find the next term in the following sequence.
The two things we need to find out are HOW the sequence changes (adddition, subtraction, multiplication, division, etc.) and by WHAT factor.
Start by finding the difference between the first two terms.
Now let's find the difference between the 2nd and 3rd given term.
Based on these two points, we can infer that this sequence changes by adding 13 to the previous term. Therefore...
the next term in the sequence is 22.
The two things we need to find out are HOW the sequence changes (adddition, subtraction, multiplication, division, etc.) and by WHAT factor.
Start by finding the difference between the first two terms.
Now let's find the difference between the 2nd and 3rd given term.
Based on these two points, we can infer that this sequence changes by adding 13 to the previous term. Therefore...
the next term in the sequence is 22.
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We have the following sequence
What is the value of 
?
We have the following sequence
What is the value of
First, find a pattern in the sequence. You will notice that each time you move from one number to the very next one, it increases by 7. That is, the difference between one number and the next is 7. Therefore, we can add 7 to 36 and the result will be 43. Thus 
.
First, find a pattern in the sequence. You will notice that each time you move from one number to the very next one, it increases by 7. That is, the difference between one number and the next is 7. Therefore, we can add 7 to 36 and the result will be 43. Thus
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Find the next term in the sequence:
2, 7, 17, 37, 77,...
Find the next term in the sequence:
2, 7, 17, 37, 77,...
The sequence follows the pattern for the equation:
Therefore,
The sequence follows the pattern for the equation:
Therefore,
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Find the next term in the following sequence.
Find the next term in the following sequence.
Determine what kind of sequence you have, i.e. whether the sequence changes by a constant difference or a constant ratio. You can test this by looking at pairs of numbers, but this sequence has a constant difference (arithmetic sequence).
So the sequence advances by subtracting 16 each time. Apply this to the last given term.
Determine what kind of sequence you have, i.e. whether the sequence changes by a constant difference or a constant ratio. You can test this by looking at pairs of numbers, but this sequence has a constant difference (arithmetic sequence).
So the sequence advances by subtracting 16 each time. Apply this to the last given term.
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Find the next term in the given arithmetic sequence:
Find the next term in the given arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
Subtract the third term from the fourth term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
Subtract the third term from the fourth term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
Subtract the third term from the fourth term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
Subtract the third term from the fourth term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the arithmetic sequence:
Find the next term in the arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the given arithmetic sequence:
Find the next term in the given arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the following arithmetic sequence:
Find the next term in the following arithmetic sequence:
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add 
to the last given number.
First, find the common difference for the sequence. Subtract the first term from the second term.
Subtract the second term from the third term.
To find the next value, add
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Find the next term in the arithmetic sequence: 
Find the next term in the arithmetic sequence:
The terms are in decreasing order, and to determine how much each number is decreasing by, we will subtract first term with the second term and the second term with the third term.
Subtract the first and second term.
Subtract the second and the third term.
Notice that each term is subtracted by five.
Subtract the third term by five to get the next term.
The answer is 
.
The terms are in decreasing order, and to determine how much each number is decreasing by, we will subtract first term with the second term and the second term with the third term.
Subtract the first and second term.
Subtract the second and the third term.
Notice that each term is subtracted by five.
Subtract the third term by five to get the next term.
The answer is
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