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If r is a constant a_n = rn for all positive integers n, for how many

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If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 27 Nov 2017, 03:27
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If r is a constant and \(a_n = rn\) for all positive integers n, for how many values of n is \(a_n < 100\)?


(1) \(a_{50} = 500\)

(2) \(a_{100} + a_{105} = 2050\)
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New post 27 Nov 2017, 03:48
If r is a constant and \(a_n = rn\) for all positive integers n, for how many values of n is \(a_n < 100\)?

(1) \(a_{50} = 500\):

Since \(a_n = rn\), then \(a_{50} =r*50= 500\). Hence, r = 10. We know everything about the sequence, so we can answer the question. Sufficient.

(2) \(a_{100} + a_{105} = 2050\):

\(100r + 105r = 2050\) --> r = 10. The same here. Sufficient.

Answer: D.
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 02 Oct 2019, 01:24
Hi Bunuel,

Thanks for the explanation.

But how did you come up with

a100+a105=2050 => 100r+105r=2050?
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New post 02 Oct 2019, 01:41
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 03 Oct 2019, 05:59
Bunuel wrote:
DealMakerOne wrote:
Hi Bunuel,

Thanks for the explanation.

But how did you come up with

a100+a105=2050 => 100r+105r=2050?


Since \(a_n = rn\), then \(a_{100} =100r\) and \(a_{105} =105r\)


Thanks so much. It's clear now.

Just simply replace a100 with 100r and a105 with 105r => 100r+105r=2050 => 205r=2050 => r=10.
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:28
Bunuel

Hi, I just have one confusion here.

The question has not specified anything regarding the construction of the equation. How did you assume that a50 = r*50?

As we can also assume r = 5 and a50 = r*25. Can you please help me understand the same.
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:30
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:33
Bunuel

My question was on this arrival - Since an=rnan=rn, then
Quote:
a50=r∗50
=500a50=r∗50=500
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:35
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:38
Bunuel

Sorry! I am still not clear. Cant r (a constant value) be anything such as 5 or 15 or (may be 10)
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Re: If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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New post 08 Oct 2019, 23:43
nehasomani33 wrote:
Bunuel

Sorry! I am still not clear. Cant r (a constant value) be anything such as 5 or 15 or (may be 10)


The stem says: \(a_n = r*n\)

If r is a constant and \(a_n = rn\) for all positive integers n, for how many values of n is \(a_n < 100\)?

(1) says: \(a_{50} = 500\). Since \(a_n = rn\), then \(a_{50} =r*50= 500\). \(r*50= 500\). Hence, r = 10.

Can you please tell me which step there is unclear?
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Re: If r is a constant a_n = rn for all positive integers n, for how many   [#permalink] 08 Oct 2019, 23:43
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