DevB wrote:In the sequence of positive numbers x1, x2, x3,..., what is the value of x1?
1. xi = (xi-1) / 2 for all integers i>1
2. x5 = x4/(x4 + 1)
Statement 1: x(i) = [x(i -1)]/2.
In other words, each term is 1/2 the value of the preceding term.
Since x� can be equal to any positive value, INSUFFICIENT.
Statement 2: xâ‚… = xâ‚„/(xâ‚„ + 1)
Here, only the relationship between xâ‚… and xâ‚„ is known.
Thus, x� can be equal to any positive value.
INSUFFICIENT.
Statements combined:
Statement 1 indicates that each term is 1/2 the preceding term, implying that xâ‚… =
xâ‚„/2.
Statement 2 indicates that xâ‚… =
xâ‚„/(xâ‚„ + 1).
Since the two expressions in red are equal to the same value, we get:
xâ‚„/2 =
xâ‚„/(xâ‚„ + 1).
Cross-multiplying, we get:
(xâ‚„)(xâ‚„ + 1) = 2xâ‚„
Since all of the values in the sequence are positive, we can safely divide each side by xâ‚„, yielding the following:
xâ‚„ + 1 = 2
xâ‚„ = 1.
Since each term is 1/2 the preceding term, we get:
x₄ = 1, x₃ = 2, x₂ = 4, x� = 8.
SUFFICIENT.
The correct answer is
C.
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