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Official 2019 Paper 1 · Q4

Paper 1Sequences & series

The sequence xnx_n is given by:

x1=10x_1=10
xn+1=xnfor n≥1x_{n+1}=\sqrt{x_n}\quad\text{for }n\geq1

What is the value of x100x_{100}?

[Note that abca^{b^c} means a(bc)a^{(b^c)}]

A1029910^{2^{99}}
B10210010^{2^{100}}
C102−9910^{2^{-99}}
D102−10010^{2^{-100}}
E10−29910^{-2^{99}}
F10−210010^{-2^{100}}
G10−2−9910^{-2^{-99}}
H10−2−10010^{-2^{-100}}

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