Arithmetic Sequences

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SSAT Upper Level Quantitative › Arithmetic Sequences

Questions 1 - 10
1

Find the term of the 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 8th term.

2

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.

3

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.

4

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.

5

Find the term of the 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 8th term.

6

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.

7

Find the term of the 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 8th term.

8

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.

9

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.

10

An arithmetic sequence begins as follows:

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

The forty-first term

The forty-second term

The forty-third term

The forty-fourth 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 forty-first term is the correct response.

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