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What is the ratio of LCM to HCF of n numbers in geometric progression with first term x and the common ratio is y?

What is the ratio of LCM to HCF of n numbers in geometric progression with first term x and the common ratio is y? Correct Answer y<sup>n – 1</sup>

Given:

The given progression is geometric progression

Formula used:

The geometric progression is as following

a, ar, ar2, ar3, ar4, ar5………. arn

Where a is the first term and r is the common ratio

Nth term of geometric progression = arn - 1

Calculation:

The first term of GP is x and common difference is y

∴ Geometric progression is as following

x, xy, xy2, xy3, xy4, xy5… xyn

Where x is the first term and y is the common ratio

Nth term of geometric progression = xyn - 1

∴ LCM of this GP = xyn – 1

And HCF of this GP = x

Now, the ratio of LCM to HCF of geometric progression

∴ LCM/HCF = xyn – 1/x = yn – 1

Hence, option (4) is correct

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