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

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Current Student
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Joined: 09 Jan 2016
Posts: 123
Location: Hong Kong
GMAT 1: 750 Q50 V41
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In a certain sequence, each term after the first term is one-half the [#permalink]

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27 May 2016, 04:46
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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
Senior Manager
Joined: 18 Jan 2010
Posts: 256
Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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27 May 2016, 05:11
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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

Intern
Joined: 18 Sep 2016
Posts: 49
Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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28 Sep 2016, 03:13
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

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Intern
Joined: 10 Sep 2014
Posts: 27
In a certain sequence, each term after the first term is one-half the [#permalink]

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10 Dec 2017, 02:49
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Joined: 02 Sep 2009
Posts: 44319
Re: In a certain sequence, each term after the first term is one-half the [#permalink]

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10 Dec 2017, 04:19
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Expert's post

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: $$0.0001 < a_{10}< 0.001$$;

$$0.0001 < 4a_{12}< 0.001$$;

$$0.000025 < a_{12}< 0.00025$$.

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Re: In a certain sequence, each term after the first term is one-half the   [#permalink] 10 Dec 2017, 04:19
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