Question

Find the two geometric means between 20 and 2500

Answer 1

Answer:

The two geometric means between 20 and 2500 are 100 and 500.

Step-by-step explanation:

First of all we all should know about a geometric progression to solve this question.

A geometric progression is a series in which there is a first term a and all the next terms are calculated by multiplying the previous term by a common number r.

where a is known as first term and

r is known as common ratio.

In the question we are given a as 20 and we have to find out 2 terms after 20 and 4th term is given as 2500.

Formula for $n^{th}$ term in a geometric progression is:

$a_{n} = a\times r^{n-1}$

Here $a_{4}$ = 2500

As per formula of $n^{th}$ term:

$a\times r^{3} = 2500\\\Rightarrow 20 \times r^{3} =2500\\\Rightarrow r^{3} = 125\\\Rightarrow r = 5$

Now, 2nd term:

$a_{2} = a \times r\\\Rightarrow a_{2} = 20 \times 5\\\Rightarrow a_{2} = 100$

Now, 3rd term:

$a_{3} = a \times r^{2} \\\Rightarrow a_{3} = 20 \times 5^{2}\\\Rightarrow a_{3} = 500$

So, the two geometric means between 20 and 2500 are 100 and 500.