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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: 08 Jan 2016
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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, 03:46
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70% (01:58) correct 30% (02:09) wrong based on 821 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 52431
Re: In a certain sequence, each term after the first term is one-half the  [#permalink]

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10 Dec 2017, 03:19
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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: $$0.0001 < a_{10}< 0.001$$;

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

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

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

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27 May 2016, 04:11
10
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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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, 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

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WE: Project Management (Manufacturing)
In a certain sequence, each term after the first term is one-half the  [#permalink]

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10 Dec 2017, 01:49
Bunuel and VeritasPrepKarishma .. Could you please help here sharing the approach? Stuck in this
Manager
Joined: 02 Jan 2016
Posts: 123
Re: In a certain sequence, each term after the first term is one-half the  [#permalink]

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16 Jun 2018, 09:41
Multiply original number 0.0001 and 0.001 with 1,00,000 both, you get:

10 and 100, divide both by 2, 5 and 50 further divide by 2, 2.5 and 25, now divide by 1,00,000 or push both numbers by five zeros, you get "C"
Manager
Joined: 02 Jan 2016
Posts: 123
In a certain sequence, each term after the first term is one-half the  [#permalink]

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16 Jun 2018, 09:43
Multiply original number 0.0001 and 0.001 with 1,00,000 both, you get:

10 and 100, divide both by 2, you get 5 and 50,
further divide 5 and 50, by 2, you get 2.5 and 25,

now divide by 1,00,000 or push both numbers by five zeros, you get "C". Tadaaaaaaaaaaaa!
In a certain sequence, each term after the first term is one-half the &nbs [#permalink] 16 Jun 2018, 09:43
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# In a certain sequence, each term after the first term is one-half the

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