### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #14 : Arithmetic Sequences

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

**Possible Answers:**

**Correct answer:**

The first term is .

The common difference is

.

The seventieth term is

.

### Example Question #15 : Arithmetic Sequences

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

The sequence has no positive terms.

The fortieth term

The thirty-ninth term

The thirty-seventh term

The thirty-eighth term

**Correct answer:**

The fortieth term

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 #16 : Arithmetic Sequences

An arithmetic sequence begins as follows:

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

**Possible Answers:**

The forty-third term

The forty-first term

The forty-fourth term

The forty-second term

The fortieth term

**Correct answer:**

The forty-first term

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 #17 : Arithmetic Sequences

An arithmetic sequence begins as follows:

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

**Possible Answers:**

The one hundred eleventh term

The one hundred twelfth term

The one hundred tenth term

The one hundred thirteenth term

The one hundred fourteenth term

**Correct answer:**

The one hundred thirteenth term

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?

**Possible Answers:**

The seventy-fifth term

The seventy-sixth term

The seventy-fourth term

The seventy-seventh term

The seventy-eighth term

**Correct answer:**

The seventy-sixth term

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?

**Possible Answers:**

The sequence has no positive terms.

The twenty-seventh term

The twenty-ninth term

The thirtieth term

The twenty-eighth term

**Correct answer:**

The twenty-ninth term

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 #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?

**Possible Answers:**

The fifty-first term

The forty-seventh term

The fiftieth term

The forty-ninth term

The forty-eighth term

**Correct answer:**

The forty-eighth term

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 #2 : 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?

**Possible Answers:**

**Correct answer:**

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 #3 : 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.

**Possible Answers:**

**Correct answer:**

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 :

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