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A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which

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Bunuel
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A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   21 Jan 2021, 22:51
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A sequence 1, 1/2, 1/4, ..., \(a_n\) is such that \(a_n=\frac{1}{2}*a_{n-1}\), then which of the following is true about \(a_{10}\)?

(A) \(0.01 < a_{10} < 0.1\)

(B) \(0.001 < a_{10} < 0.01\)

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

(D) \(0.00001 < a_{10} < 0.0001\)

(E) \(0.000001 < a_{10} < 0.00001\)


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A geometric sequence 1, 1/2 ……an is such that an=1/2*a(n-1), then a10 will fall in which of the following value range?
(A) 0.01-0.1
(B) 0.001-0.01
(C) 0.0001-0.001
(D) 0.00001-0.0001
(E) 0.000001-0.00001
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B
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QuantMadeEasy
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   21 Jan 2021, 23:59
Each subsequent term of the sequence is multiplied by 1/2

a1 = 1
a2 = 1/2
a3 = 1/2^2
a4 = 1/2^3
Similarly a10 = 1/2^9 = 1/512 = 2/1024

Value of 1/ 1024 ~ 1/1000 ~ 0.001

Therefore value of 2/1024 ~ 2 * 0.001 ~ 0.002

B is correct
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B
ginevrafratto
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   22 Jan 2021, 01:57
QuantMadeEasy wrote:
Each subsequent term of the sequence is multiplied by 1/2

a1 = 1
a2 = 1/2
a3 = 1/2^2
a4 = 1/2^3
Similarly a10 = 1/2^9 = 1/512 = 2/1024

Value of 1/ 1024 ~ 1/1000 ~ 0.001

Therefore value of 2/1024 ~ 2 * 0.001 ~ 0.002

B is correct


Sorry, why if a10=1/512 we do multiply by 2 to get 2/1024?
thank you
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   22 Jan 2021, 04:30
ginevrafratto wrote:
QuantMadeEasy wrote:
Each subsequent term of the sequence is multiplied by 1/2

a1 = 1
a2 = 1/2
a3 = 1/2^2
a4 = 1/2^3
Similarly a10 = 1/2^9 = 1/512 = 2/1024

Value of 1/ 1024 ~ 1/1000 ~ 0.001

Therefore value of 2/1024 ~ 2 * 0.001 ~ 0.002

B is correct


Sorry, why if a10=1/512 we do multiply by 2 to get 2/1024?
thank you

2 is multiplied just to make denominator closer to 1000 for ease of calculation

You may also do the calculations as 1/512 ~ 1/500 ~ 0.002 (approx)
Hope this helps :)
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Lodz697
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   23 Mar 2024, 08:51
Why the answer is not C?

If 1/1000 = 0,001, 1/1024 must be smaller than 0,001...

Where am I wrong?

Bunuel
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink] New post   24 Mar 2024, 04:31
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Lodz697 wrote:
A sequence 1, 1/2, 1/4, ..., \(a_n\) is such that \(a_n=\frac{1}{2}*a_{n-1}\), then which of the following is true about \(a_{10}\)?


(A) \(0.01 < a_{10} < 0.1\)

(B) \(0.001 < a_{10} < 0.01\)

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

(D) \(0.00001 < a_{10} < 0.0001\)

(E) \(0.000001 < a_{10} < 0.00001\)

Why the answer is not C?

If 1/1000 = 0,001, 1/1024 must be smaller than 0,001...

Where am I wrong?

Bunuel

­

\(a_1=\frac{1}{2^0}=1\),

\(a_2=\frac{1}{2^1}=\frac{1}{2}\),

\(a_3=\frac{1}{2^2}=\frac{1}{4}\),

\(a_4=\frac{1}{2^3}=\frac{1}{8}\),

...

\(a_n=\frac{1}{2^{n-1}}\).

Hence, \(a_{10}\) is not \(\frac{1}{2^{10}}=\frac{1}{1,024}\), it's \(\frac{1}{2^{9}}=\frac{1}{512}=\frac{2}{1,024} \)­, which is a bit less than 0.002, making B the answer.

Holpe it helps.­
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Re: A sequence 1, 1/2, 1/4, ..., an is such that an=1/2*a(n-1), then which [#permalink]
24 Mar 2024, 04:31
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