Question

In a certain sequence, the term $x_n$ is given by the formula $x_n=2x_{n-1}-\frac{1}{2}\left(x_{n-2}\right)$ for all $n\ge 2$ . If $x_0=3$, what is the value of $x_3$ if $x_1=2$ ?

• A. $2.5$
• B. $3.125$
• C. $4$
• D. $5$
• E. $6.75$

Answer 1

The correct option is C $4$

Given equation is $x_n=2x_{n-1}-\frac{1}{2}\left(x_{n-2}\right)$

Also given $x_0=3$

We need to find value of $x_3$ if $x_1=2$

$x_2=2x_1-\frac{1}{2}\left(x_0\right)$

$\Rightarrow x_2=2\times 2-\frac{1}{2}\left(3\right)$

$\Rightarrow x_2=4-\frac{3}{2}$

$\Rightarrow x_2=2.5$

Here $x_3=2x_2-\frac{1}{2}\left(x_1\right)$

$\Rightarrow x_3=2\times 2.5-\frac{1}{2}\left(2\right)$

$\Rightarrow x_3=5-1=4$