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GMAT Math Practice - Geometric Progression

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Question 5

Medium Problem Solving Concepts Covered1. Sum of first 'n' terms of a geometric progression.
2. Common ratio of a geometric progression.
2 concepts

The GMAT Math practice question given below is a sequences and series question. Concept covered is sum of a Geometric Progression and its common ratio.

Statistics
5
Geometric Progression
If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?
  1. 3
  2. 1/3
  3. 2
  4. 9
  5. 1/9
Correct Answer     Choice C. The common ratio is 2.

Explanatory Answer

Forumula to find the sum of first 'n' terms of a GP

The sum of the first n terms of a G.P. is given by , where 'a' is the first term of the G.P., 'r' is the common ratio and 'n' is the number of terms in the G.P.
Therefore, the sum of the first 6 terms of the G.P will be equal to
And sum of the first 3 terms of the G.P. will be equal to

Use the ratio between these two sums to find 'r'

The ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1
i.e.

Or r3 + 1 = 9
r3 = 8
r = 2

Choice C is the correct answer.

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