Question

If f(n+1)=f(n)-8if f(1)=100what is f(6)

Answer 1

The value of $f(6)$ is $f(6)=60$

Explanation:

The equation is $f(n+1)=f(n)-8$

It is given that $f(1)=100$

Now, we shall determine the value of $f(6)$

Let us substitute $n=1,2,3,4,5$ in the equation $f(n+1)=f(n)-8$

For $n=1$,

$\begin{aligned}f(1+1) &=f(1)-8 \\f(2) &=100-8 \\&=92\end{aligned}$

Thus, when $n=1$ ⇒ $f(2)=92$

For $n=2$,

$\begin{aligned}f(2+1) &=f(2)-8 \\f(3) &=92-8 \\&=84\end{aligned}$

Thus, when $n=2$ ⇒ $f(3)=84$

For $n=3$ ,

$\begin{aligned}f(3+1) &=f(3)-8 \\f(4) &=84-8 \\&=76\end{aligned}$

Thus, when $n=3$ ⇒ $f(4)=76$

For $n=4$,

$\begin{aligned}f(4+1) &=f(4)-8 \\f(5) &=76-8 \\&=68\end{aligned}$

Thus, when $n=4$ ⇒ $f(5)=68$

For $n=5$,

$\begin{aligned}f(5+1) &=f(5)-8 \\f(6) &=68-8 \\&=60\end{aligned}$

Thus, when $n=5$ ⇒ $f(6)=60$

Hence, the value of $f(6)$ is $f(6)=60$