GRE Math : Common Difference in Sequences
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Example Question #1 : How To Find The Common Difference In Sequences
The sequence 
What is the difference between the 20th and the 30th elements of 
The answer cannot be determined
For this sequence, you do not have a starting point (i.e. 
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 
Example Question #1 : How To Find The Common Difference In Sequences
Which of the following defines any term in a linear sequence having 
Since this sequence is linear, we know that it will add the same amount for each element. This means that you can evenly divide the difference between the first and the ninth term. Be careful! There will be eight total increases between these terms. (Think this through: 1 to 2, 2 to 3, 3 to 4, etc.)
Thus, we know that the total difference between these terms is:
Now, dividing this among the eight increases that happen, we know:
This means that for each element, we add 
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