# SSAT Upper Level Math : Sequences and Series

## Example Questions

### 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 fortieth term

The forty-first term

The forty-third term

The forty-fourth term

The forty-second 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 #2 : 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 tenth term

The one hundred fourteenth term

The one hundred twelfth term

The one hundred eleventh term

The one hundred thirteenth 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 #3 : 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-fourth term

The seventy-eighth term

The seventy-sixth 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 #4 : 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 thirtieth term

The twenty-seventh term

The twenty-eighth term

The twenty-ninth 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.

### Example Question #5 : 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 fifty-first term

The forty-eighth term

The forty-seventh term

The forty-ninth term

The fiftieth 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 #6 : How To Find The 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 #7 : How To Find The Nth Term Of An Arithmetic Sequence

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

Explanation:

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

Since the eleventh and thirteenth 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 #1601 : Ssat Upper Level Quantitative (Math)

The lengths of the sides of ten squares form an arithmetic sequence. One side of the smallest square measures eight inches; one side of the second-smallest square measures one foot.

Give the area of the largest square.

2,304 square inches

484 square inches

576 square inches

784 square inches

1,936 square inches

1,936 square inches

Explanation:

Let  be the lengths of the sides of the squares in inches.  and , so their common difference is

The arithmetic sequence formula is

The length of a side of the largest square - square 10 - can be found by substituting :

The largest square has sides of length 44 inches, so its area is the square of this, or  square inches.

### Example Question #1602 : Ssat Upper Level Quantitative (Math)

An arithmetic sequence begins as follows:

Give the thirty-second term of this sequence.

Explanation:

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

The initial term in the given sequence is

;

the common difference is

;

We are seeking term .

This term is

### Example Question #1611 : Ssat Upper Level Quantitative (Math)

An arithmetic sequence begins as follows:

Give the thirty-third term of this sequence.

The correct answer is not given among the other four responses.

The correct answer is not given among the other four responses.

Explanation:

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

.

The initial term in the given sequence is

;

the common difference is

.

We are seeking term .

Therefore,

,

which is not among the choices.