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Question 115

A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1​,x2​,x3​,… is defined by

x1=2,x2=9xn=xn−1+xn−2,n≥3 \begin{aligned}x_1 &= 2, x_2 = 9 \\x_n &= x_{n-1} + x_{n-2}, \quad n \geq 3\end{aligned} x1​xn​​=2,x2​=9=xn−1​+xn−2​,n≥3​

Find x3,x4 x_3, x_4\,x3​,x4​ and x5x_5x5​.

[3]

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