SSAT Upper Level Math : How to find the answer to an arithmetic sequence

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : How To Find The Answer To An Arithmetic Sequence

The angle measures of a pentagon form an arithmetic sequence. The smallest angle measures . What does the largest angle measure?

Possible Answers:

Correct answer:

Explanation:

The measures of the five angles of a pentagon add up to , based on the formula .

If the measures of the five angles form an arithmetic sequence, the angles have measures increasing by a some common difference, .

 

Given this pattern and the total sum, we can solve for the common difference.

The greatest of the angle measures is given by .

Example Question #2 : How To Find The Answer To An Arithmetic Sequence

Hunter makes  for the first hour of work,  for his second hour of work,  for his third hour of work, and so on. How much money will he make if he works for  hours?

Possible Answers:

Correct answer:

Explanation:

The question is basically asking you to find the sum of the first  terms of the following arithmetic sequence:

 

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 11th 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 11th term.

Now that we know the 11th term of the sequence, we can plug in that value into the equation for the sum to find what these first 11 terms add up to.

Example Question #3 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the arithmetic sequence:

Possible Answers:

Correct answer:

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.

Example Question #4 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the following arithmetic sequence:

Possible Answers:

Correct answer:

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 16th term.

Example Question #5 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the following arithmetic sequence:

Possible Answers:

Correct answer:

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 9th term.

Example Question #6 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the following arithmetic sequence:

Possible Answers:

Correct answer:

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 12th term.

Example Question #7 : How To Find The Answer To An Arithmetic Sequence

Find the  term for the following arithmetic sequence:

Possible Answers:

Correct answer:

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 : How To Find The Answer To An Arithmetic Sequence

Find the  term of the following arithmetic sequence:

Possible Answers:

Correct answer:

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 : How To Find The Answer To An Arithmetic Sequence

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?

Possible Answers:

Correct answer:

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 #34 : Sequences And Series

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?

Possible Answers:

Correct answer:

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.

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