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

1 Answer
mason m
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)#.

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