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If
f(1)=6 and
f(n+1)=-5f(n)+2 then find the value of
f(3).
Answer:

If $f(1)=6$ and $f(n+1)=-5 f(n)+2$ then find the value of $f(3)$ . $\newline$ Answer:

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Evaluate exponential functions

Full solution

Q. If

f(1)=6

and

f(n+1)=-5 f(n)+2

then find the value of

f(3)

.

\newline

Answer:

Given Data: We are given $f(1)=6$ and the recursive formula $f(n+1)=-5f(n)+2$ . To find $f(3)$ , we first need to find $f(2)$ .
Find $f(2)$ : Using the recursive formula, we substitute $n=1$ to find $f(2)$ .
$f(2) = -5f(1) + 2$
$f(2) = -5(6) + 2$
$f(2) = -30 + 2$
$f(2) = -28$
Find $f(3)$ : Now that we have $f(2)$ , we use it to find $f(3)$ by substituting $n=2$ into the recursive formula. $f(3) = -5f(2) + 2$ $f(3) = -5(-28) + 2$ $f(3) = 140 + 2$ $f(3) = 142$

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