What is the ratio of LCM to HCF of n numbers in geometric progression

1.	What is the ratio of LCM to HCF of n numbers in geometric progression with first term x and the common ratio is y?1. xyn – 12. yn – 1 xn – 13. xn yn – 14. yn – 1
Answer» Correct Answer - Option 4 : y^{n – 1} 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 = ar^{n - 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 = xy^{n - 1} ∴ LCM of this GP = xy^{n – 1} And HCF of this GP = x Now, the ratio of LCM to HCF of geometric progression ∴ LCM/HCF = xy^{n – 1}/x = y^{n – 1} Hence, option (4) is correct

What is the ratio of LCM to HCF of n numbers in geometric progression with first term x and the common ratio is y?1. xyn – 12. yn – 1 xn – 13. xn yn – 14. yn – 1

Answer» Correct Answer - Option 4 : y^{n – 1}

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 = ar^{n - 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 = xy^{n - 1}

∴ LCM of this GP = xy^{n – 1}

And HCF of this GP = x

Now, the ratio of LCM to HCF of geometric progression

∴ LCM/HCF = xy^{n – 1}/x = y^{n – 1}

Hence, option (4) is correct

Discussion

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