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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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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, 03:48
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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) \(a_{50} = 500\):

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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If r is a constant a_n = rn for all positive integers n, for how many &nbs [#permalink] 27 Nov 2017, 03:48
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