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`

Step-by-step 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`