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# In the sequence of positive numbers x1, x2, x3, ..., what is the value

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Director
Joined: 18 Dec 2017
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Re: In the sequence of positive numbers x1, x2, x3, ..., what is the value  [#permalink]

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04 Nov 2019, 15:41
testprep2010 wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$

Well,
This question appeared in Official Free Test #2 (my attempt 2) and This is not how statement 1 was formatted. $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

Please find attached image. I treated Statement 1 as xi-1 and marked the answer as E.

Is it just me or it is actually confusing in the official test?

bb Bunuel chetan2u
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Re: In the sequence of positive numbers x1, x2, x3, ..., what is the value  [#permalink]

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04 Nov 2019, 17:06
TheNightKing wrote:
testprep2010 wrote:
In the sequence of positive numbers $$x_1$$, $$x_2$$, $$x_3$$, ..., what is the value of $$x_1$$?

(1) $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

(2) $$x_5=\frac{x_4}{x_4+1}$$

Well,
This question appeared in Official Free Test #2 (my attempt 2) and This is not how statement 1 was formatted. $$x_i=\frac{x_{(i-1)}}{2}$$ for all integers $$i>1$$.

Please find attached image. I treated Statement 1 as xi-1 and marked the answer as E.

Is it just me or it is actually confusing in the official test?

bb Bunuel chetan2u

Hi

You are likely to find it in the same way
But you should look at the size of font of numbers. When it is i-1 and x_4+1, the size of 1 differs. It is bigger when it is a separate term.
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Re: In the sequence of positive numbers x1, x2, x3, ..., what is the value  [#permalink]

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04 Nov 2019, 17:11
Quote:
Hi

You are likely to find it in the same way
But you should look at the size of font of numbers. When it is i-1 and x_4+1, the size of 1 differs. It is bigger when it is a separate term.

Sure. Thank you!
I will be careful from next time and make sure I think twice before solving.
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In the sequence of positive numbers x1, x2, x3, ..., what is the value  [#permalink]

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24 Nov 2019, 13:39
Hi Bunuel

Could i assume per S2

$$X_3$$ = $$\frac{X_3}{X_3+1}$$ as well ?

Per S2 -- $$X_4$$ = $$\frac{X_4}{X_4+1}$$

So, I thought this trend could be applied to others as well. I.e.

$$X_3$$ = $$\frac{X_2}{X_2+1}$$

$$X_2$$ = $$\frac{X_1}{X_1+1}$$

or does this apply to $$X_4$$ only ?
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Posts: 59722
Re: In the sequence of positive numbers x1, x2, x3, ..., what is the value  [#permalink]

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24 Nov 2019, 23:58
jabhatta@umail.iu.edu wrote:
Hi Bunuel

Could i assume per S2

$$X_3$$ = $$\frac{X_3}{X_3+1}$$ as well ?

Per S2 -- $$X_4$$ = $$\frac{X_4}{X_4+1}$$

So, I thought this trend could be applied to others as well. I.e.

$$X_3$$ = $$\frac{X_2}{X_2+1}$$

$$X_2$$ = $$\frac{X_1}{X_1+1}$$

or does this apply to $$X_4$$ only ?

No, you cannot assume that. The second statement does not give you a formula for nth term of the sequence (while the first statement does).
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Re: In the sequence of positive numbers x1, x2, x3, ..., what is the value   [#permalink] 24 Nov 2019, 23:58

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# In the sequence of positive numbers x1, x2, x3, ..., what is the value

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