ACT Math : How to find the next term in an arithmetic sequence

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #23 : Sequences

Given the sequence of numbers: 

1, 5, 9, _ , _ , 21 ....

What are the two missing terms of the arithmetic sequence?

Possible Answers:

13, 16

12, 18

14, 17

13, 17

14, 16

Correct answer:

13, 17

Explanation:

The sequence is defined by a= 4n – 3  for such n = 1,2,3,4....

Example Question #3 : Nth Term Of An Arithmetic Sequence

What is the next term in the following sequence?

Possible Answers:

Correct answer:

Explanation:

What is the next term in the following sequence?

This is an arithmetic sequence with a common difference of . To find the next term in an arithmetic sequence, add the common difference to the previously listed term:

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Find the sixth term in the following number sequence. 

Possible Answers:

Correct answer:

Explanation:

This question can be answered by analyzing the sequence provided and determining the pattern. The first term is , and the second term is  The third term is Thus,  has been added to  in order to obtain , and  has been added to  in order to obtain  This shows that  is added to each preceding term in the sequence in order to obtain the next term. The complete sequence from terms one through six is shown below.

Thus, the sixth term is   

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

What is the next term of the series ?

Possible Answers:

Correct answer:

Explanation:

Begin by looking at the transitions from number to number in this series:

From  to : Add 

From  to : Subtract 

From  to : Add 

From  to : Subtract 

From what you can tell, you can guess that the next step will be to add . Thus, the next value will be .

Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

What is the next term in the following sequence: ?

Possible Answers:

Correct answer:

Explanation:

This sequence is a little tricky. Notice that the second element is equal to the first. After that, the third is equal to the sum of the first two , next the fourth is equal to the sum of the second and the third , and the same continues for each element after this. Thus, the next element in the series will be equal to  or .

Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

What is the next term in the sequence?

Possible Answers:

Correct answer:

Explanation:

The difference between each term is constant, thus the sequence is an arithmetic sequence.

Simply find the difference between each term, and add it to the last term to find the next term.

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