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If
f(1)=3 and
f(n)=-4f(n-1)-2 then find the value of
f(3).
Answer:

If $f(1)=3$ and $f(n)=-4 f(n-1)-2$ then find the value of $f(3)$ . $\newline$ Answer:

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Evaluate exponential functions

Full solution

Q. If

f(1)=3

and

f(n)=-4 f(n-1)-2

then find the value of

f(3)

.

\newline

Answer:

Find $f(2)$ : We are given $f(1)=3$ . To find $f(3)$ , we first need to find $f(2)$ using the recursive formula $f(n)=-4f(n-1)-2$ . $\newline$ Substitute $n=2$ into the formula to find $f(2)$ . $\newline$ $f(2) = -4f(2-1) - 2$ $\newline$ $f(2) = -4f(1) - 2$ $\newline$ $f(2) = -4(3) - 2$ $\newline$ $f(1)=3$ $0$ $\newline$ $f(1)=3$ $1$
Find $f(3)$ : Now that we have $f(2) = -14$ , we can use it to find $f(3)$ using the same recursive formula. $\newline$ Substitute $n=3$ into the formula to find $f(3)$ . $\newline$ $f(3) = -4f(3-1) - 2$ $\newline$ $f(3) = -4f(2) - 2$ $\newline$ $f(3) = -4(-14) - 2$ $\newline$ $f(3) = 56 - 2$ $\newline$ $f(3) = 54$

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