Chapter 11.3, Problem 39PPS

To determine

Find two geometric means between $3\text{and}375$

Answer to Problem 39PPS

Two geometric means are: $15,75$

Explanation of Solution

Given:

First and last terms are $3\text{and}375$

Concept Used:

Since there are two terms between the first and last term, there are 2+2= 4 total terms, so n = 4

Now find the common difference.

Calculation:

Now find the common difference.

  $\begin{array}{l}{a}_1=3\text{and}{a}_4=375;\text{find}r\\ a_4=a_1·r^{4-1}=a_1·r^3\\ 375=3·r^3\\ \frac{375}{3}=\frac{3}{3}·r^3\\ r^3=125=5^3\\ r=5\end{array}$

  $\begin{array}{l}{a}_1=3;r=5,\text{Find}{a}_2,a_3,\\ a_2=a_1·r=3·5=15\\ a_3=a_2·r=15·5=75\end{array}$

Two geometric means are: $15,75$

Thus, two geometric means are: $15,75$