# GRE Math : Common Difference in Sequences

## Example Questions

### Example Question #102 : Arithmetic

The sequence  is defined as:

What is the difference between the 20th and the 30th elements of ?

Explanation:

For this sequence, you do not have a starting point (i.e. ); however, you are able to interpret it relatively easily. The sequence is merely one in which each number is twenty larger than the one preceding it. Therefore, if  were , you would have:

Now, to find difference between the 20th and the 30th element, it is merely necessary to count the number of twenties that would be added for each of those elements. For instance, the difference between the 21st and the 20th elements is . Thus, since you would add a total of ten twenties from the 20th to the 30th element, you know that the difference between these two values is .

### Example Question #2 : How To Find The Common Difference In Sequences

Which of the following defines any term in a linear sequence having  for its first term and  for its ninth term?