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In the sequence above, each term after the first 1/2 of the preceding

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xmagedo
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In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  29 Jul 2010, 23:37
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240, 120, 60, 30

In the sequence above, each term after the first 1/2 of the preceding term. What is the least term of the sequence is greater than 1 ?

A. 32/15
B. 16/15
C. 15/8
D. 15/4
E. 15/2
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Bunuel
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Re: In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  29 Jul 2010, 23:57
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xmagedo wrote:
240,120,60,30

In the sequnce above, each term after the first 1/2 of the preceding term. What is the least term of the sequnce is greater than 1 ?

a 32/15
b 16/15
c 15/8
d 15/4
e 15/2

pleas help with a formula


There is no need for formula:
240, 120, 60, 30, 30/2, 30/4, 30/8, 30/16, 30/32<1. So the leas term more than 1 is 30/16=15/8.

But still if you need: \(\frac{30}{2^n}>1\), where n is integer --> \(2^n<30\) --> \(n<5\) --> \(n=4\) --> \(\frac{30}{2^n}=\frac{30}{2^4}=\frac{15}{8}\).

Answer: C.
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Re: In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  05 Oct 2019, 17:02
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xmagedo wrote:
240,120,60,30

In the sequence above, each term after the first 1/2 of the preceding term. What is the least term of the sequence is greater than 1 ?

A. 32/15
B. 16/15
C. 15/8
D. 15/4
E. 15/2


After 30, we have:

15, 15/2, 15/4, 15/8, 15/16.

Since 15/16 is not greater than 1, we see that the smallest number in the sequence greater than 1 is 15/8.

Answer: C
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Re: In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  29 Nov 2016, 09:19
xmagedo wrote:
240,120,60,30

In the sequence above, each term after the first 1/2 of the preceding term. What is the least term of the sequence is greater than 1 ?

A. 32/15
B. 16/15
C. 15/8
D. 15/4
E. 15/2


Greater than 1 = Numerator > Denominator

Now, go fearlessly- 30, 15 , 15/2 , 15/4 , 15/8, 15/16

Hence, the answer can be found in 10 seconds and it is (C)
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jotapepe
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Re: In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  12 Oct 2021, 16:01
I found it easier to just do:

...15...

Following term is 15/2 ... then (15/2)/2 = basically is just 15/2 times the reciprocal of 2 aka. 1/2 = 15/4


then you take 15/4 and divide it by 2 again or multiply it by the reciprocal of 2 (1/2) and you get 15/8
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Re: In the sequence above, each term after the first 1/2 of the preceding [#permalink] New post  20 Dec 2022, 09:20
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