GRE Math : How to find the answer to an arithmetic sequence

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Arithmetic Sequences

What is the sum of the odd integers ?

Possible Answers:

None of the other answers

Correct answer:


Do NOT try to add all of these.  It is key that you notice the pattern.  Begin by looking at the first and the last elements: 1 and 99.  They add up to 100.  Now, consider 3 and 97.  Just as 1 + 99 = 100, 3 + 97 = 100.  This holds true for the entire list.  Therefore, it is crucial that we find the number of such pairings.

1, 3, 5, 7, and 9 are paired with 99, 97, 95, 93, and 91, respectively.  Therefore, for each 10s digit, there are 5 pairings, or a total of 500.  To get all the way through our numbers, you will have to repeat this process for the 10s, 20s, 30s, and 40s (all the way to 49 + 51 = 100).

Therefore, there are 500 (per pairing) * 5 pairings = 2500.

Example Question #31 : Integers

A sequence is defined by the following formula:

What is the 4th element of this sequence?

Possible Answers:

Correct answer:


With series, you can always "walk through" the values to find your answer. Based on our equation, we can rewrite  as :

You then continue for the third and the fourth element:

Example Question #3 : Arithmetic Sequences

What is the sum of the 40th and the 70th elements of the series defined as:

Possible Answers:

Correct answer:


When you are asked to find elements in a series that are far into its iteration, you need to find the pattern. You absolutely cannot waste your time trying to calculate all of the values between  and . Notice that for every element after the first one, you subtract . Thus, for the second element you have:

For the third, you have:

Therefore, for the 40th and 70th elements, you will have:

The sum of these two elements is:

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