# SSAT Upper Level Math : Sequences and Series

## Example Questions

### Example Question #7 : Arithmetic Sequences

Find the  term for 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 7th term.

### Example Question #8 : 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 10th term.

### Example Question #9 : Arithmetic Sequences

Brandon is improving very quickly at math. He improves at a rate of  points per test. If he scored a  on his first test,  on his second test, and  on his third test, what score will he get on his  test?

Explanation:

You should recognize this as an arithmetic sequence:

The question is asking you to find the 8th 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 8th term.

### Example Question #10 : Arithmetic Sequences

Julia gets better every time she plays basketball. In her first game, she scored  points. In her second game, she scored  points, and in her third game, she scored  points. If she continues to improve her basketball skills at this same pace, how many points should she be scoring by her  game?

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 #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 #33 : 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 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 #2 : How To Find The 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 : 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 fortieth term

The thirty-seventh term

The thirty-ninth 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.