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In the sequence of positive numbers X1, X2, X3, ..., what is the value of X1?

1) X(i) = X(i-1)/2 2) X(5) = X(4)/X(4)+1

1) tells us nothing of the values of the terms
2) tells us nothing of the sequence

together:

from 1: Each term is half of the preceeding term.
from 2: the only way for this stmt to be true and to follow the seqyence is if x(4) = 1. Therefore, x(1) = 8.

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).

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