# SSAT Upper Level Math : Arithmetic Sequences

## Example Questions

### Example Question #31 : Sequences And Series

Leon makes  for the first hour of work,  for his second hour of work,  for his third hour of work, and so on. How much will he make for his  hour of work?

Explanation:

You should recognize this as an arithmetic sequence:

The question is asking you to find the 12th term in this particular 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 12th term.

### Example Question #32 : Sequences And Series

Find the sum of the first  terms of the following arithmetic sequence:

Explanation:

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 8th 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 8th term.

Now that we know the 8th term of the sequence, we can plug in that value into the equation for the sum to find what these first 8 terms add up to.

### Example Question #11 : Other Arithmetic Sequences

Find the sum of the first  terms of the following arithmetic sequence:

Explanation:

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 9th 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 9th term.

Now that we know the 9th term of the sequence, we can plug in that value into the equation for the sum to find what these first 9 terms add up to.

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

The first two terms of an arithmetic sequence are 1,000 and 997, in that order. What is the seventieth term?

Explanation:

The first term is .

The common difference is

.

The seventieth term is

.

### Example Question #1 : Nth Term Of An Arithmetic Sequence

The first two terms of an arithmetic sequence are 4 and 9, in that order. Give the one-hundredth term of that sequence.

Explanation:

The first term is ; the common difference is

.

The hundredth term is

.

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

An arithmetic sequence begins as follows:

Which of the following terms is the first positive term in the sequence?

The thirty-seventh term

The thirty-ninth term

The fortieth term

The sequence has no positive terms.

The thirty-eighth term

The fortieth term

Explanation:

The common difference of the sequence is

,

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The first positive term is the fortieth term.

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

An arithmetic sequence begins as follows:

Which of the following is the first term greater than 100?

The forty-third term

The forty-second term

The forty-fourth term

The forty-first term

The fortieth term

The forty-first term

Explanation:

The common difference of the sequence is

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The forty-first term is the correct response.

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

An arithmetic sequence begins as follows:

Which of the following terms is the first negative term in the sequence?

The one hundred thirteenth term

The one hundred tenth term

The one hundred fourteenth term

The one hundred eleventh term

The one hundred twelfth term

The one hundred thirteenth term

Explanation:

The common difference of the sequence is

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The first negative term is the one hundred thirteenth term.

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

An arithmetic sequence begins as follows:

Which of the following terms is the first negative term in the sequence?

The seventy-fifth term

The seventy-sixth term

The seventy-eighth term

The seventy-fourth term

The seventy-seventh term

The seventy-sixth term

Explanation:

The common difference of the sequence is

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The seventy-sixth term is the first negative term.

### Example Question #1 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

Which of the following terms is the first positive term in the sequence?

The twenty-ninth term

The twenty-eighth term

The thirtieth term

The twenty-seventh term

The sequence has no positive terms.

The twenty-ninth term

Explanation:

The common difference of the sequence is

,

so the th term of the sequence is

To find out the minimum value for which , set up this inequality:

The first positive term in the sequence is the twenty-ninth term.