Related Rates: the Expanding Balloon Problem
How to Calculate a Sequence's Terms by Using the Sequence Expression
How to Use Differentiation to Calculate the Maximum Area of a Corral

How to Identify a Term in a Geometric Sequence When You Know Consecutive Terms

If your pre-calculus teacher gives you consecutive terms in a geometric sequence and asks you to identify another term in the sequence, the steps you will follow to find this term are remarkably similar to those for arithmetic sequences. You find the common ratio (not the difference!), you write the specific formula for the given sequence, and then you find the term you're looking for.

An example of a geometric sequence is 2, 4, 8, 16, 32. To find the 15th term, follow these steps:

  1. Find the common ratio, r.

    In this sequence, each consecutive term is twice the previous term. If you can't see the common ratio by looking at the sequence, divide any term by the term before it.

  2. Find the formula for the given sequence.

    In terms of the formula, a1 = 2 and r = 2. The general formula for this sequence is

    image0.png

    which simplifies (using the rules of exponents) to

    image1.png
  3. Find the term you're looking for.

    If an = 2n, then a15 = 215 = 32,768.

The formula in this example simplifies nicely because the bases of the two exponents are the same. If the first term and r don't have the same base, you can't combine them.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Use Differentiation to Calculate the Maximum Volume of a Box
Related Rates: the Trough of Swill Problem
How to Identify a Term in a Geometric Sequence When You Know Two Nonconsecutive Terms
How to Recognize Recursive Arithmetic Sequences
Related Rates: Two Cars at a Crossroads
Advertisement

Inside Dummies.com