Bunuel
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 \(i>1\) --> we have the general formula connecting two consecutive terms (basically we have geometric progression with common ratio 1/2), but without the value of any term this info is insufficient to find \(x_1\).
(2) \(x_5=\frac{x_4}{x_4+1}\) --> we have the relationship between \(x_5\) and \(x_4\), also insufficient to find \(x_1\) (we cannot extrapolate the relationship between \(x_5\) and \(x_4\) to all consecutive terms in the sequence).
(1)+(2) From (1) \(x_5=\frac{x_4}{2}\) --> \(\frac{x_4}{2}=\frac{x_4}{x_4+1}\) --> \(x_4=1\) --> \(x_4=1=x_1*(\frac{1}{2})^3\) --> \(x_1=8\). Sufficient.
Answer: C.
Bunuel I got this wrong because I thought x1 = 0 is also a solution. But since the question says it is a
sequence of positive numbers, I guess I cannot assume that.
On a slightly different note, can the values in a sequence be a constant?