Sequence Problems

For sequence problems on the GRE, you may be asked to do any of the following:

• Determine which answer choice corresponds to the correct definition (or rule) for a sequence (direct or recursive).
• Determine the value of a particular item in a sequence.

• Determine the sum or difference of a set of items in a sequence.

For simple linear sequences, in which the same number is added to any term to yield the next term, you can use the following alternative method—rather than find the rule or definition for the sequence, you can sometimes logically derive one item in the sequence based on the information given:

If each number in a sequence is three more than the previous number, and the sixth number is 32, what is the 100th number?

Instead of finding the rule for this sequence, consider the following reasoning:

From the sixth term to the one hundredth term, there are 94 “jumps” of 3. Because 94 × 3 = 282, there is an increase of 282 from the sixth term to the one hundredth term:

• 32 + 282 = 314

Check Your Skills

8. If each number of a sequence is 4 more than the previous number, and the 3rd number in the sequence is 13, what is the 114th number in the sequence?