# SAT Math : Sequences

## Example Questions

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

Solve each problem and decide which is the best of the choices given.

Find the sixth term in the following arithmetic sequence.

Explanation:

First find the common difference of the sequence,

Thus there is a common difference of

between each term,

so follow that pattern for another  terms, and the result is .

### Example Question #6 : How To Find The Next Term In An Arithmetic Sequence

Find the missing number in the sequence:

Explanation:

The pattern of this sequence is  where  represents the position of the number in the sequence.

for the first number in the sequence.

for the second number.

For the fourth term, . Therefore,

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

An arithmetic sequence begins as follows:

Express the next term of the sequence in simplest radical form.

Explanation:

Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:

The common difference  of an arithmetic sequence can be found by subtracting the first term from the second:

Add this to the second term to obtain the desired third term:

.

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

An arithmetic sequence begins as follows:

Give the next term of the sequence in simplest radical form.

None of the other choices gives the correct response.

None of the other choices gives the correct response.

Explanation:

Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.

The common difference  of an arithmetic sequence can be found by subtracting the first term from the second:

Setting :

Add this to the second term to obtain the desired third term:

This is not among the given choices.

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

An arithmetic sequence begins as follows:

Give the sixth term of the sequence in decimal form.

Explanation:

The common difference  of an arithmetic sequence can be found by subtracting the first term from the second:

Setting :

The th term  of an arithmetic sequence can be derived using the formula

Setting :

The decimal equivalent of this can be found by dividing 13 by 15 as follows:

The correct choice is .

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

An arithmetic sequence begins as follows:

Give the sixth term of the sequence.

Explanation:

The common difference  of an arithmetic sequence can be found by subtracting the first term from the second:

Setting :

The th term  of an arithmetic sequence can be derived using the formula

Setting

### Example Question #21 : Nth Term Of An Arithmetic Sequence

Complete the sequence:

Explanation:

The pattern of this sequence is  where  represents the place of each number in the order of the sequence.

Here are our givens:

, our first term.

, our second term.

, our third term.

This means that our fourth term will be:

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