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# In the sequence of non-zero numbers t1, t2,t3,......tn,.....

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In the sequence of non-zero numbers t1, t2,t3,......tn,..... [#permalink]

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12 Jul 2008, 22:34
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In the sequence of non-zero numbers t1, t2,t3,......tn,.....,tn+1 =tn/2 for all positive integers of n. What is the value of t5?

(1) t3 = 1/4
(2) t1 - t5 = 15/16

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-1-2-4-8-16-32-each-term-after-the-104175.html
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12 Jul 2008, 23:02
riks200 wrote:
In the sequence of non-zero numbers t1, t2,t3,......tn,.....,tn+1 =t2/2 for all positive integers of n. What is the value of t5?
1. t3=1/4
2. t1-t5=15/16

Pls Explain?

is the question a complete one? seems the question is not complete for me.

what is equal to t2/2?
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12 Jul 2008, 23:51
there is a typo in the question, refer 7-t66979
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Re: In the sequence of non-zero numbers t1, [#permalink]

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23 Aug 2013, 03:14
correction: tn+1 =tn/2

1) SUFFICIENT: t3=1/4 hence t4=1/4/2=1/8 and t5=1/8/2=1/16
2) SUFFICIENT: t1-(t1/2/2/2/2)=15/16 -> t1-(t1/16)=15/16 -> t1=1

If anybody has questions can write to me: laura81@blu.it (I teach GMAT in MILANO)
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In the sequence of non-zero numbers t1, t2,t3,......tn,..... [#permalink]

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23 Aug 2013, 03:25
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riks200 wrote:
In the sequence of non-zero numbers t1, t2,t3,......tn,.....,tn+1 =tn/2 for all positive integers of n. What is the value of t5?

(1) t3 = 1/4
(2) t1 - t5 = 15/16

Given: $$t_{n+1}=\frac{t_n}{2}$$. So $$t_2=\frac{t_1}{2}$$, $$t_3=\frac{t_2}{2}=\frac{t_1}{4}$$, $$t_4=\frac{t_3}{2}=\frac{t_1}{8}$$, ...

Basically we have geometric progression with common ratio $$\frac{1}{2}$$: $$t_1$$, $$\frac{t_1}{2}$$, $$\frac{t_1}{4}$$, $$\frac{t_1}{8}$$, ... --> $$t_n=\frac{t_1}{2^{n-1}}$$.

Question: $$t_5=\frac{t_1}{2^4}=?$$

(1) $$t_3=\frac{1}{4}$$ --> we can get $$t_1$$ --> we can get $$t_5$$. Sufficient.
(2) $$t_1-t_5=2^4*t_5-t_5=\frac{15}{16}$$ --> we can get $$t_5$$. Sufficient.

Generally for arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.

Hope it helps.
OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-sequence-1-2-4-8-16-32-each-term-after-the-104175.html
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In the sequence of non-zero numbers t1, t2,t3,......tn,.....   [#permalink] 23 Aug 2013, 03:25
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