Answer:
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 [tex]n^{th}[/tex] term in a geometric progression is:
[tex]a_{n} = a\times r^{n-1}[/tex]
Here [tex]a_{4}[/tex] = 2500
As per formula of [tex]n^{th}[/tex] term:
[tex]a\times r^{3} = 2500\\\Rightarrow 20 \times r^{3} =2500\\\Rightarrow r^{3} = 125\\\Rightarrow r = 5[/tex]
Now, 2nd term:
[tex]a_{2} = a \times r\\\Rightarrow a_{2} = 20 \times 5\\\Rightarrow a_{2} = 100[/tex]
Now, 3rd term:
[tex]a_{3} = a \times r^{2} \\\Rightarrow a_{3} = 20 \times 5^{2}\\\Rightarrow a_{3} = 500[/tex]
So, the two geometric means between 20 and 2500 are 100 and 500.
