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

## Example Questions

### Example Question #1 : Sequences

What is the sum of the odd integers ?

Explanation:

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 #2 : Other Arithmetic Sequences

A sequence is defined by the following formula:

What is the 4th element of this sequence?

Explanation:

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 #2 : Sequences

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