# SSAT Upper Level Math : Sequences and Series

## Example Questions

### Example Question #21 : Sequences And Series

Find the common difference for the arithmetic sequence:

Explanation:

Subtract the first term from the second term to find the common difference.

### Example Question #13 : Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Explanation:

Subtract the first term from the second term to find the common difference.

### Example Question #11 : Common Difference In Sequences

Find the common difference for the arithmetic sequence:

Explanation:

Subtract the first term from the second term to find the common difference.

### Example Question #21 : Sequences And Series

Find the common difference for the arithmetic sequence:

Explanation:

Subtract the first term from the second term to find the common difference.

### Example Question #1 : Arithmetic Sequences

The angle measures of a pentagon form an arithmetic sequence. The smallest angle measures . What does the largest angle measure?

Explanation:

The measures of the five angles of a pentagon add up to , based on the formula .

If the measures of the five angles form an arithmetic sequence, the angles have measures increasing by a some common difference, .

Given this pattern and the total sum, we can solve for the common difference.

The greatest of the angle measures is given by .

### Example Question #1 : Arithmetic Sequences

Hunter makes  for the first hour of work,  for his second hour of work,  for his third hour of work, and so on. How much money will he make if he works for  hours?

Explanation:

The question is basically asking you to find the sum of the first  terms of the following arithmetic sequence:

To find the sum of a certain number of terms in an arithmetic sequence, use the following formula:

•  the number of the terms you have
•  the first term of the sequence
•  term of the sequence

To find the sum, we need to first find the 11th term of the sequence.

To find any term in an arithmetic sequence, use the following formula:

•  is the term we want to find
•  is the first term of the sequence
•  is the number of the term we want to find
•  is the common difference

Using the information given from the question,

Now, plug in the information to find the value of the 11th term.

Now that we know the 11th term of the sequence, we can plug in that value into the equation for the sum to find what these first 11 terms add up to.

### Example Question #1 : Other Arithmetic Sequences

Find the  term of the arithmetic sequence:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

•  is the term we want to find
•  is the first term of the sequence
•  is the number of the term we want to find
•  is the common difference

For this sequence,

Now, plug in the information to find the value of the 8th term.

### Example Question #1 : Arithmetic Sequences

Find the  term of the following arithmetic sequence:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

•  is the term we want to find
•  is the first term of the sequence
•  is the number of the term we want to find
•  is the common difference

For this sequence,

Now, plug in the information to find the value of the 16th term.

### Example Question #1 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the following arithmetic sequence:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

•  is the term we want to find
•  is the first term of the sequence
•  is the number of the term we want to find
•  is the common difference

For this sequence,

Now, plug in the information to find the value of the 9th term.

### Example Question #21 : Sequences And Series

Find the  term of the following arithmetic sequence:

Explanation:

To find any term in an arithmetic sequence, use the following formula:

•  is the term we want to find
•  is the first term of the sequence
•  is the number of the term we want to find
•  is the common difference

For this sequence,

Now, plug in the information to find the value of the 12th term.