# Algebra 1 : Sequences

## Example Questions

### Example Question #11 : 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 #12 : 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 #13 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the 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 #14 : 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 #15 : 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 #16 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the arithmetic sequence:

Explanation:

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.

### Example Question #3481 : Algebra 1

Find the next term in the following sequence.

Explanation:

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.

### Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

The first term of an arithmetic sequence is ; the fifth term is . What is the second term?

Explanation:

To find the common difference , use the formula .

For us, is and is .

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.

Explanation:

Let  be the common difference, and let  be the second term. The first three terms are, in order, .

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: . Since the second and fourth terms are 37 and 49, respectively, we can solve for the common difference.

The common difference is 6. The first term is .

### Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins with . If  is the first term in the sequence, find the 31st term.