Related Rates: the Trough of Swill Problem
How to Find the General Formula for the nth Term of an Arithmetic Sequence Using Any Two Terms
How to Find the nth Term Using the First Terms of an Arithmetic Sequence

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

If your pre-calculus teacher gives you any two nonconsecutive terms of a geometric sequence, you can find the general formula of the sequence as well as any specified term. For example, if the 5th term of a geometric sequence is 64 and the 10th term is 2, you can find the 15th term. Just follow these steps:

  1. Determine the value of r.

    You can use the geometric formula to create a system of two formulas to find r:




    You can use substitution to solve one equation for a1:


    Plug this expression in for a1 in the other equation:


    Now simplify this equation:

  2. Find the specific formula for the given sequence.

    1. a.Plug r into one of the equations to find a1.

      This step gives you

    2. b.Plug a1 and r into the formula.

      Now that you know a1 and r, you can write the formula:

  3. Find the term you're looking for.

    In this case, you want to find the 15th term (n = 15):


Here's another example: The annual depreciation of a car's value is approximately 30 percent. Thus, every year, the car is actually worth 70 percent of its value from the year before. If a1 represents the value of a car when it was new and n represents the number of years that have passed,


Notice that this sequence starts at 0, which is okay as long as the information says that it starts at 0.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
How to Use Differentiation to Calculate the Maximum Volume of a Box
How to Calculate a Sequence's Terms by Using the Sequence Expression
How to Recognize Recursive Arithmetic Sequences
Related Rates: Two Cars at a Crossroads
How to Use Differentiation to Calculate the Maximum Area of a Corral