Answer to Question #136983 in Discrete Mathematics for Rakibul

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

There is the mistake in the question. We don't know $f(n-2), n=1.$

I think that the correct question is as follows:

The recursive definition of a function X is given as:

f(0)=5 and f(n)=f(n-1)+5

Now, find out the value of f(14) using the above function.

$f(0)=5$

$f(n)=f(n-1)+5, n\geq1$

$f(1)=f(0)+5=5+5=10=5+5(1)$

$f(2)=f(1)+5=10+5=15=5+5(2)$

$f(3)=f(2)+5=15+5=20=5+5(3)$

$f(4)=f(3)+5=20+5=25=5+5(4)$

$f(5)=f(4)+5=25+5=30=5+5(5)$

$f(6)=f(5)+5=30+5=35=5+5(6)$

$f(7)=f(6)+5=35+5=40=5+5(7)$

$f(8)=f(7)+5=40+5=45=5+5(8)$

$f(9)=f(8)+5=45+5=50=5+5(9)$

$f(10)=f(9)+5=50+5=55=5+5(10)$

$f(11)=f(10)+5=55+5=60=5+5(11)$

$f(12)=f(11)+5=60+5=65=5+5(12)$

$f(13)=f(12)+5=65+5=70=5+5(13)$

$f(14)=f(13)+5=70+5=75=5+5(14)$

$f(14)=75$