# 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:

Determine the value of

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

*r*:or

You can use substitution to solve one equation for

*a*_{1}:Plug this expression in for

*a*_{1}in the other equation:Now simplify this equation:

Find the specific formula for the given sequence.

a.Plug

*r*into one of the equations to find*a*_{1}*.*This step gives you

b.Plug

*a*_{1}*r*into the formula.Now that you know

*a*_{1}and*r,*you can write the formula:

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 *a*_{1} 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.