# SSAT Upper Level Math : nth Term of an Arithmetic Sequence

## Example Questions

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### Example Question #1 : 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 #2 : 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 #3 : 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 fortieth term

The thirty-eighth term

The thirty-ninth term

The sequence has no positive terms.

The thirty-seventh 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 #4 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

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

The fortieth term

The forty-first term

The forty-fourth term

The forty-second term

The forty-third 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 #5 : 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 eleventh term

The one hundred thirteenth term

The one hundred fourteenth term

The one hundred twelfth term

The one hundred tenth 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 : 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-seventh term

The seventy-sixth term

The seventy-eighth term

The seventy-fifth term

The seventy-fourth 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 #7 : 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-seventh term

The twenty-eighth term

The sequence has no positive terms.

The thirtieth term

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.

### Example Question #8 : 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-eighth term

The fiftieth term

The fifty-first term

The forty-seventh term

The forty-ninth term

The forty-eighth 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 correct response is the forty-eighth term.

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

The tenth and twelfth terms of an arithmetic sequence are 8.4 and 10.2. What is its first term?

Explanation:

The th term of an arithmetic sequence with initial term  and common difference  is defined by the equation

Since the tenth and twelfth terms are two terms apart, the common difference can be found as follows:

Now, we can set  in the sequence equation to find :

### Example Question #10 : Nth Term Of An Arithmetic Sequence

The eleventh and thirteenth terms of an arithmetic sequence are, respectively, 11 and 14. Give its first term.