# Algebra 1 : Sequences

## Example Questions

### Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

In the following arithmetic sequence, what is ?

7

5

2

6

6

Explanation:

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 .

### Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Given the sequence below, what is the sum of the next three numbers in the sequence?

Explanation:

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.

### Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

We have the following sequence

What is the value of ?

Explanation:

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 .

### Example Question #1 : Sequences

Find the next term in the sequence:

2, 7, 17, 37, 77,...

Explanation:

The sequence follows the pattern for the equation:

Therefore,

### Example Question #5 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following sequence.

Explanation:

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.

### Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Explanation:

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.

### Example Question #7 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Explanation:

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.

### Example Question #8 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the given arithmetic sequence:

Explanation:

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.

### Example Question #9 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

Explanation:

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.

### Example Question #10 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence: