GRE Math : How to find the nth term of an arithmetic sequence

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Nth Term Of An Arithmetic Sequence

The first term in a sequence of integers is 2 and the second term is 10. All subsequent terms are the arithmetic mean of all of the preceding terms. What is the 39th term?

Possible Answers:

5

1200

6

300

600

Correct answer:

6

Explanation:

The first term and second term average out to 6. So the third term is 6. Now add 6 to the preceding two terms and divide by 3 to get the average of the first three terms, which is the value of the 4th term. This, too, is 6 (18/3)—all terms after the 2nd are 6, including the 39th. Thus, the answer is 6.

Example Question #2 : Nth Term Of An Arithmetic Sequence

Consider the following sequence of integers:

5, 11, 23, 47

What is the 6th element in this sequence?

Possible Answers:

None of the other answers

95

189

93

191

Correct answer:

191

Explanation:

First, consider the change in each element.  Notice that in each case, a given element is twice the preceding one plus one:

11 = 2 * 5 + 1

23 = 11 * 2 + 1

47 = 23 * 2 + 1

 

To find the 6th element, continue following this:

The 5th: 47 * 2 + 1 = 95

The 6th: 95 * 2 + 1 = 191

Example Question #3 : Nth Term Of An Arithmetic Sequence

The sequence  begins with the numbers  and has the  term defined as , for .

What is the value of the  term of the sequence?

Possible Answers:

Correct answer:

Explanation:

The first term of the sequence is , so here , and we're interested in finding the 20th term, so we'll use n = 20.

Plugging these values into the given expression for the nth term gives us our answer.

and

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

In a sequence of numbers, the first two values are 1 and 2. Each successive integer is calculated by adding the previous two and mutliplying that result by 3. What is fifth value in this sequence?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Our sequence begins as 1, 2.

Element 3: (Element 1 + Element 2) * 3 = (1 + 2) * 3 = 3 * 3 = 9

Element 4: (Element 2 + Element 3) * 3 = (2 + 9) * 3 = 11 * 3 = 33

Element 5: (Element 3 + Element 4) * 3 = (9 + 33) * 3 = 42 * 3 = 126

Example Question #5 : Nth Term Of An Arithmetic Sequence

Let Z represent a sequence of numbers  wherein each term is defined as seven less than three times the preceding term.  If , what is the first term in the sequence?

Possible Answers:

Correct answer:

Explanation:

Let us first write the value of a consecutive term in a numerical format:

Consequently,

Using the first equation, we can define  in terms of :

This allows us to rewrite

as

Rearrangement of terms allows us to solve for :

Now, using our second equation, we can find , the first term:

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