Question

Suppose that f (n + 1) = $\frac{2f\left(n\right)+1}{2}$ for $n=1,2,3,...$ and$\left(1\right)=2$ Then $f\left(101\right)$ equals

• A. $50$
• B. $52$
• C. $54$
• D. none of these

Answer 1

The correct option is B $52$

From given relation, we can find $f\left(n\right)$

given $f\left(1\right)=2.$ so, $f\left(2\right)=5/2,f\left(3\right)=3,f\left(4\right)=7/2,.......$so on

By observing the values we can predict the actual function

$f\left(n\right)=(n+3)/2$

So,$f\left(101\right)=52$