How do you find the 10th term in the geometric sequence 25, 5, 1, 0.2, ...?

1 Answer
Nov 14, 2015

Write an exponential equation.

Explanation:

Each term of the geometric sequence is 1/5 the previous term. Therefore, you can say that each term is the previous term multiplied by 5^-1. We can write an equation that models this, starting at 25, where x is the number term in the sequence.

f(x)=25(5)^-(x-1)

With this equation, the first term would be calculated so: f(x)=25(5)^-(1-1)=25(5)^-0=25*1=25

Finding the tenth term: f(x)=25(5)^-(10-1)=25(5)^-9=25/(5^9)=(5^2)/(5^9)=color(blue)(1/(5^7)).

This is equal to color(red)(0.0000128).