How to find the next term in an arithmetic sequence - Algebra

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.

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 .

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.

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.

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 .

The sequence follows the pattern for the equation:

Therefore,

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.

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 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 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 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 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 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 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 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 to the last given number.

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 .

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.

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 .

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.