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Nataliya [291]
3 years ago
8

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

Mathematics
1 answer:
Irina18 [472]3 years ago
4 0

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

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