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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.

Re: In the sequence of non-zero numbers t1, t2,t3,......tn,..... [#permalink]
23 Aug 2013, 02:25

1

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Expert's post

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.

Answer: D.

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

- any particular two terms, - any particular term and common difference (common ratio), - any particular term and the formula for n_th term, - 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.