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# Geometric Progression and Integers | PRMO 2017 | Question 5 Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and integers.

## Geometric Progression and Integers - PRMO 2017

Let u,v,w be real numbers in geometric progression such that u>v>w. Suppose $u^{40}=v^{n}=w^{60}$, find value of n.

• is 107
• is 48
• is 840
• cannot be determined from the given information

### Key Concepts

Geometric series

Integers

Algebra

PRMO, 2017, Question 5

Higher Algebra by Hall and Knight

## Try with Hints

First hint

Let u=a, v=ar, w=$ar^{2}$

then $a^{40}$=$(ar)^{n}$=$(ar^{2})^{60}$

Second Hint

$\Rightarrow a^{20}=r^{-120}$

$\Rightarrow a=r^{-6}$

Final Step

and $r^{-240}=r^{-5n}$

$\Rightarrow 5n=240$

$\Rightarrow n=48$.

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Try this beautiful problem from the Pre-RMO, 2017 based on Geometric Progression and integers.

## Geometric Progression and Integers - PRMO 2017

Let u,v,w be real numbers in geometric progression such that u>v>w. Suppose $u^{40}=v^{n}=w^{60}$, find value of n.

• is 107
• is 48
• is 840
• cannot be determined from the given information

### Key Concepts

Geometric series

Integers

Algebra

PRMO, 2017, Question 5

Higher Algebra by Hall and Knight

## Try with Hints

First hint

Let u=a, v=ar, w=$ar^{2}$

then $a^{40}$=$(ar)^{n}$=$(ar^{2})^{60}$

Second Hint

$\Rightarrow a^{20}=r^{-120}$

$\Rightarrow a=r^{-6}$

Final Step

and $r^{-240}=r^{-5n}$

$\Rightarrow 5n=240$

$\Rightarrow n=48$.

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