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

Given Initial Condition: We are given the initial condition f(1) = 1. We need to use the recursive formula f(n) = -2f(n-1) + 3 to find f(5).Find f(2): First, let's find f(2) using the recursive formula and the initial condition f(1) = 1. f(2) = -2f(1) + 3 = -2(1) + 3 = -2 + 3 = 1.Find f(3): Next, we'll find f(3) using the value of f(2) we just found. f(3) = -2f(2) + 3 = -2(1) + 3 = -2 + 3 = 1.Find f(4): Now, let's find f(4) using the value of f(3). f(4) = -2f(3) + 3 = -2(1) + 3 = -2 + 3 = 1.Find f(5): Finally, we'll find f(5) using the value of f(4). f(5) = -2f(4) + 3 = -2(1) + 3 = -2 + 3 = 1.

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

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

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Precalculus

Find the roots of factored polynomials

Full solution

Q. If

f(1)=1

and

f(n)=-2 f(n-1)+3

then find the value of

f(5)

\newline

Answer:

Given Initial Condition: We are given the initial condition $f(1) = 1$ . We need to use the recursive formula $f(n) = -2f(n-1) + 3$ to find $f(5)$ .
Find $f(2)$ : First, let's find $f(2)$ using the recursive formula and the initial condition $f(1) = 1$ .
$f(2) = -2f(1) + 3 = -2(1) + 3 = -2 + 3 = 1$ .
Find $f(3)$ : Next, we'll find $f(3)$ using the value of $f(2)$ we just found. $f(3) = -2f(2) + 3 = -2(1) + 3 = -2 + 3 = 1$ .
Find $f(4)$ : Now, let's find $f(4)$ using the value of $f(3)$ . $f(4) = -2f(3) + 3 = -2(1) + 3 = -2 + 3 = 1$ .
Find $f(5)$ : Finally, we'll find $f(5)$ using the value of $f(4)$ . $f(5) = -2f(4) + 3 = -2(1) + 3 = -2 + 3 = 1$ .