Answer to Question #137266 in Discrete Mathematics for Raziya Sultana

Question

The recursive definition of a function X is given as:
f(0)=5 and f(n)=f(n-2)+5
Now, find out the value of f(14) using the above function.

Answer 1

$\mathbf{Given : f(0)=5\;and\;f(n)=f(n-2)+5}\\ \\ \\ \\ \\ \mathbf{To\;find:\;f(14)}$

$\mathbf{Put\;n=14\;in\;the\;recursive\;definition\;of\;function}$

$\mathbf{we \;get-}$

$\mathbf{\therefore f(14)=f(14-2)+5=f(12)+5}\\ \\ \mathbf{\implies f(14)=(f(12-2)+5)+5=f(10)+10}\\ \\ \mathbf{\implies f(14)=(f(10-2)+5)+10=f(8)+15}\\ \\ \mathbf{\implies f(14)=(f(8-2)+5)+15=f(6)+20}\\ \\ \mathbf{\implies f(14)=(f(6-2)+5)+20=f(4)+25}\\ \\ \mathbf{\implies f(14)=(f(4-2)+5)+25=f(2)+30}\\ \\ \mathbf{\implies f(14)=(f(2-2)+5)+30=f(0)+35}\\ \\ \mathbf{\implies f(14)=5+35=40\;\;(\because\; f(0)=5)}\\ \\ \mathbf{\therefore f(14)=40}$