Just, AP

Algebra Level 4

If the 2 nd 2^\text{nd} , 5 th 5^\text{th} and 9 th 9^\text{th} of a non-constant arithmetic progression follows an geometric progression , what is the common ratio of this geometric progression?

Give your answer to 2 decimal places.


The answer is 1.33.

Rishabh Sood by Rishabh Sood , 20, India

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2 solutions

Ahmed Hossain
May 31, 2016

a + 4 d a + d \frac{a+4d}{a+d} = a + 8 d a + 4 d \frac{a+8d}{a+4d} or, 3 d a + d \frac{3d}{a+d} = 4 d a + 4 d \frac{4d}{a+4d} ;[dividendo] thus, a + 4 d a + d \frac{a+4d}{a+d} = 4 3 \frac{4}{3} =1.33

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Hats off, thanks for posting the solution. Please provide a feedback for the question if possible.

Rishabh Sood - 5 years ago
Rishabh Sood
May 25, 2016

T e r m 2 Term_{2} = a+d

T e r m 5 Term_{5} = a+4d

T e r m 9 Term_{9} = a+8d

As, T e r m 2 Term_{2} , T e r m 5 Term_{5} and T e r m 9 Term_{9} are in GP:

( a + 4 d ) 2 (a+4d)^{2} =(a+d)(a+8d)

=> d(8d-a)=0

Also, as AP is non-constant, d ≠ \neq 0

=> a=8d

=> AP: 8d,9d,10d...........

=> Common ratio of GP: t e r m 5 t e r m 2 \frac{term_{ 5}}{term_ {2}} = 12 d 9 d \frac{12d}{9d} =1.3(approx)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Solved it the same way nice question (+1)

Ashish Menon - 5 years ago

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Thank you , bro

Rishabh Sood - 5 years ago

As our decimal evaluation allows for a 2% margin of error, I've edited the answer to be accurate to 3 significant figures.

Calvin Lin Staff - 5 years ago

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