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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.

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), - 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.

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