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If
f(1)=1 and
f(n)=-5f(n-1)-n then find the value of
f(3).
Answer:

If $f(1)=1$ and $f(n)=-5 f(n-1)-n$ then find the value of $f(3)$ . $\newline$ Answer:

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Evaluate exponential functions

Full solution

Q. If

f(1)=1

and

f(n)=-5 f(n-1)-n

then find the value of

f(3)

.

\newline

Answer:

Given $f(1)=1$ : We are given $f(1)=1$ . To find $f(3)$ , we first need to find $f(2)$ using the recursive formula $f(n)=-5f(n-1)-n$ . Substitute $n=2$ into the formula to find $f(2)$ . $f(2) = -5f(2-1) - 2$ $f(2) = -5f(1) - 2$ $f(2) = -5(1) - 2$ $f(1)=1$ $0$ $f(1)=1$ $1$
Find $f(2)$ : Now that we have $f(2) = -7$ , we can use it to find $f(3)$ using the same recursive formula. $\newline$ Substitute $n=3$ into the formula to find $f(3)$ . $\newline$ $f(3) = -5f(3-1) - 3$ $\newline$ $f(3) = -5f(2) - 3$ $\newline$ $f(3) = -5(-7) - 3$ $\newline$ $f(3) = 35 - 3$ $\newline$ $f(3) = 32$

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