Chapter 11.3, Problem 3CYU

To determine

Write an equation for the nth term of the geometric series $18,6,2,\mathrm{....}$

Answer to Problem 3CYU

  $a_n=a_1·r^{n-1}=18·{(\frac{1}{3})}^{n-1}$

Explanation of Solution

Given: The series $18,6,2,\mathrm{....}$

Concept Used:

General equation for the nth term of any geometric series is $a_n=a_1·r^{n-1}$

Where $a_1$ the first term and r is is the common ratio.

Calculation:

  $a_1=18;\text{Common}\text{ratio}=r=\frac{\text{2nd}\text{term}}{\text{1st}\text{term}}=\frac{6}{18}=\frac{1}{3}$

  $a_n=a_1·r^{n-1}=18·{(\frac{1}{3})}^{n-1}$

Thus, nth term of the series $18,6,2,\mathrm{....}$ is $a_n=a_1·r^{n-1}=18·{(\frac{1}{3})}^{n-1}$