Formulas Defining Term Values for Geometric Sequences In the previous example we explored the number by which we must multiply when we make a large "jump" from one position to a later position. Let's generalize this idea and show how to get the value of the nth term from the common ratio and a 1 . Formula for geometric sequences To go from the 1st term in the sequence to the n th term in the sequence we change the term position by n 1 (we take n 1 "steps", or make a "jump" that moves n 1 terms). Every "step" changes the term value by multiplying by r (the common ratio), so changing the term position by n 1 means we must multiply by r a total of n 1 times, or multiply a 1 by r n 1 to get a n . Therefore, a n = a 1 r n 1 . The Formula for a Geometric Sequence's Term Values If a geometric sequence has a common ratio of r , then any term value a n can be represented as follows (where a 1 is the value