Question 82

In a certain sequence the term $$x_{n}$$ is given by formula $$x_{n}=5x_{n-1} - \frac{3}{4}x_{n-2}$$ for $$n\geq2$$. What is the value of $$x_{3}$$, if $$x_{0}=4$$ and $$x_{1}=2?$$

Solution

Given that $$x_{n}=5x_{n-1} - \frac{3}{4}x_{n-2}$$

$$\therefore$$ $$x_{2}=5x_{1} - \frac{3}{4}x_{0}$$

$$x_{2}=5*2 - \frac{3}{4}*4$$ = $$10-3$$ = 7

Similarly $$x_{3}=5x_{2} - \frac{3}{4}x_{1}$$

$$x_{3}=5*7 - \frac{3}{4}*2$$ = 35 - $$\frac{3}{2}$$ = $$\frac{67}{2}$$

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