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Problem
N.B: This problem is for SAT Subject Math Level 2
\(If \quad x_0 \quad and \quad x_{x+1} = \sqrt {4 + x_n}, \quad then \quad x_3 = \)
(A) 2.65
(B) 2.58 (C) 2.56 (D) 2.55 (E) 2.54 Solution
Answer is C.
This is a simple but tricky problem. It is simple to apply but you have to think recursively. For n = 0, we have:
\(x_{0+1} = \sqrt {4 + x_0} \)
\(x_1 \quad = \quad \sqrt {4 + 3} \quad = \quad \sqrt{7} \quad = \quad 2.65 \)
\(x_2 \quad = \quad \sqrt {4 + x_1} \quad = \quad \sqrt {4 + 2.65} \quad = \quad 2.58 \)
\(x_3 \quad = \quad \sqrt {4 + x_2} \quad = \quad \sqrt{4 + 2.58} \quad = \quad 2.56\)
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