Maths
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# Geometric Progression Problems with Solutions

Learn about Geometric Progression through solving examples. If stuck, check out the solutions under them.

5 minutes long
Posted by Tanwir Silar, 4/8/2021 Hesap Oluştur

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Read here to learn about Geometric progression. In this blog, we are going to learn few approaches of solving Geometric Progression problems with solutions.

## Solved problems on Geometric Progression

Example 1:
Find the 20th and nth terms of the G.P. Solution:
We have the first two terms of the G.P: a1 = 5/2, a2 = 5/4.
Common ratio of the G.P, r = an/an-1 = a2/a1 = Formula for the nth term of G.P. is, an = arn-1, where a = first term, r = common ratio.
Therefore, 20th term Example 2:
Evaluate Solution:
The given summations can be written as two summations. The first summations adds the number 2 eleven times. So, the value of the summation = 11 x 2 = 22.
The second summation can be expanded as This is a G.P. with first term, a = 3 and r = a2/a1 = 9/3 = 3.
We need to find the sum of first 11 terms of it. The formula for the sum of first n terms of a G.P. is Substituting the values of a, r, n in it, gives us : The result of the second summations is 265719.
Answer = first summation + second summation
= 22 + 265719

#### More Examples:

Example 3:
The sum of first three terms of a G.P. is 39/10 and their product is 1. Find the common ratios and the terms.
Solution:
Note: When we are given the product of odd number (2n + 1) of terms of a G.P. It is preferred to take the sequence as . By taking the terms as stated when the product of all of the terms is taken, we are left with a2n+1, which reduces our effort significantly.
In the questions, we are given first three terms of G.P. So we consider the terms as .
We know that the sum of the terms is 39/10 and the product of the terms is 1, ⇒ a3 = 1 ⇒ a = 1. (real solution)
Now solving for using the equation of sum, we get: Substituting the values in the expression we get the solutions as r = 0.4 or r = 2.5.
For r = 0.4 and a = 1, the terms of the G.P. are 1/0.4, 1, 0.4 = 2.5, 1, 0.4 .
For r = 2.5 and a = 1, the terms of the G.P. are 1/2.5, 1, 2.5 = 0.4, 1, 2.5 .

The above three approaches can be used to get solutions for a ton of problems on Geometric Progression.