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

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Intern
Joined: 14 Sep 2017
Posts: 34
Location: Italy
If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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27 Nov 2017, 03:27
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15% (low)

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80% (01:34) correct 20% (01:54) wrong based on 130 sessions

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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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Joined: 02 Sep 2009
Posts: 49858
If r is a constant a_n = rn for all positive integers n, for how many  [#permalink]

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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.

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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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