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In a certain sequence, each term after the first term is one-half the

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In a certain sequence, each term after the first term is one-half the [#permalink]

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In a certain sequence, each term after the first term is one-half the previous term. If the tenth term of the sequence is between 0.0001 and 0.001, then the twelfth term of the sequence is between

(A) 0.0025 and 0.025
(B) 0.00025 and 0.0025
(C) 0.000025 and 0.00025
(D) 0.0000025 and 0.000025
(E) 0.00000025 and 0.0000025
[Reveal] Spoiler: OA

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Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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12th Term will be obtained by multiplying the 10th term by \(\frac{1}{2}\) * \(\frac{1}{2}\)

Let 10th term is a

0.0001 < \(a_{10}\) < 0.001

12th term will be

\(\frac{0.0001}{4}\) < \(a_{12}\) < \(\frac{0.001}{4}\)

0.000025 < \(a_{12}\) < 0.00025

Option C is the answer

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Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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New post 28 Sep 2016, 02:13
the low limit of the number is equal to 1/10 of the highter limit of the number.

if you divide the low limit you'll find 0.000025

as a consequence the high limit of the number will be the low one *10 = 0.00025

answer C
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In a certain sequence, each term after the first term is one-half the [#permalink]

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New post 10 Dec 2017, 01:49
Bunuel and VeritasPrepKarishma .. Could you please help here sharing the approach? Stuck in this :(

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Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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New post 10 Dec 2017, 03:19
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sadikabid27 wrote:
Bunuel and VeritasPrepKarishma .. Could you please help here sharing the approach? Stuck in this :(


In a certain sequence, each term after the first term is one-half the previous term. If the tenth term of the sequence is between 0.0001 and 0.001, then the twelfth term of the sequence is between

(A) 0.0025 and 0.025
(B) 0.00025 and 0.0025
(C) 0.000025 and 0.00025
(D) 0.0000025 and 0.000025
(E) 0.00000025 and 0.0000025

Each term after the first term is one-half the previous term: \(a_{n+1}=\frac{a_n}{2}\). So:

\(a_{11}=\frac{a_{10}}{2}\)

\(a_{12}=\frac{a_{11}}{2}=\frac{a_{10}}{4}\) --> \(4a_{12}=a_{10}\).


Given: \(0.0001 < a_{10}< 0.001\);

\(0.0001 < 4a_{12}< 0.001\);

\(0.000025 < a_{12}< 0.00025\).

Answer: C.
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Re: In a certain sequence, each term after the first term is one-half the   [#permalink] 10 Dec 2017, 03:19
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