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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.

Re: In the sequence of positive numbers x1, x2, x3, ..., what [#permalink]
20 Jan 2014, 09:39

Expert's post

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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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