To solve number pattern problems, start by observing the entire pattern from beginning to end. Decide if the numbers are increasing or decreasing. Next, try to figure out if the numbers change by adding, multiplying, subtracting or dividing a static or changing number.
Isolate the first three or four numbers in the pattern and try to discover what relationship they have to each other. For example, are the numbers increasing by the same number amount, such as all numbers increasing by seven, or do they increase by a growing number amount such as two, three or four? Take notes on observations of the first four numbers, and then apply the same pattern theories to the rest of the sequence.
Another way to test the pattern you have observed is to create a sequence that starts with the first four numbers. If the sequence matches the original pattern, the theory is correct. If not, apply the other theories until you find the right pattern. Finish the problem by writing out the pattern in words. For example, if the number increases by seven each time, write, "each number in the sequence is added to the number seven to produce the next number."