Chapter 11, Problem 13MCQ

To determine

Find 3 geometric means between 0.5 and 2048

Answer to Problem 13MCQ

Option J is correct.

Explanation of Solution

Given: Find 3 geometric means between 0.5 and 2048 Concept Used:

The nth term of GP series: $a_n=a_1·r^{n-1}$

Calculation:

  $\begin{array}{l}{a}_1=0.5,a_5=2048;\text{find}r\\ a_n=a_1·r^{n-1}\\ 2048=0.5·r^{5-1}\\ \frac{2048}{0.5}=r^4=4096\\ r^4=4096=8^4\\ r=8\end{array}$

  $\begin{array}{l}{a}_1=0.5,r=8;\text{find}{a}_2,a_3,a_4\\ a_2=a_1·r=0.5·8=4\\ a_3=a_2·r=4·8=32\\ a_4=a_3·r=32·8=256\\ 4,32,256\end{array}$

Thus, option J is correct.