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M16-26

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M16-26 [#permalink]

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New post 16 Sep 2014, 00:59
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The sequence \(a_1\), \(a_2\), \(a_3\), ..., \(a_n\), ... is such that \(a_{n}-a_{n+1}=a_{n+1}\) for all integers \(n \ge 1\). What is the value of fourth element of this sequence?


(1) The first element of this sequence is 1

(2) The third element of this sequence is \(\frac{1}{4}\)

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Re M16-26 [#permalink]

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New post 16 Sep 2014, 00:59
Official Solution:


Given that \(a_{n}-a_{n+1}=a_{n+1}\). So, \(a_{n+1}=\frac{a_{n}}{2}\).

(1) The first element of this sequence is 1. Given: \(a_1=1\). Now, since \(a_{n+1}=\frac{a_{n}}{2}\) then \(a_2=\frac{a_1}{2}=\frac{1}{2}\), \(a_3=\frac{a_2}{2}=\frac{1}{4}\) and \(a_4=\frac{a_3}{2}=\frac{1}{8}\). Sufficient.

(2) The third element of this sequence is \(\frac{1}{4}\). Given: \(a_3=\frac{1}{4}\), hence \(a_4=\frac{a_3}{2}=\frac{1}{8}\). Sufficient.


Answer: D
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Re: M16-26 [#permalink]

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New post 25 Mar 2017, 01:01
Hi bunuel please explain how u got an/2.i cudnt undertstand the calculation thank you

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Re: M16-26 [#permalink]

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Re: M16-26 [#permalink]

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New post 25 Mar 2017, 04:04
Hi bunuel i am talking about this part : Given that an-an+1=an+1 so, an+1= an/2 this part i am not able to configure please be kind to let me know how you got an+1=an/2 thank you

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Re: M16-26 [#permalink]

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New post 25 Mar 2017, 06:05
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matayo25 wrote:
Hi bunuel i am talking about this part : Given that an-an+1=an+1 so, an+1= an/2 this part i am not able to configure please be kind to let me know how you got an+1=an/2 thank you

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Please use math formulas. Here is how: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

As for your question:

Given that \(a_{n}-a_{n+1}=a_{n+1}\).

Add \(a_{n+1}\) to both parts: \(a_{n}=2*a_{n+1}\).

So, \(a_{n+1}=\frac{a_{n}}{2}\).

It's very basic algebraic manipulation. The same as below example:

x - y = y;

y = x/2.

Hope it's clear.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M16-26 [#permalink]

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New post 25 Mar 2017, 06:22
Thanks a lot bunuel

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Re: M16-26   [#permalink] 25 Mar 2017, 06:22
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