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

Given Function and Initial Value: We are given f(1)=1. To find f(3), we first need to find f(2) using the recursive formula f(n)=-2f(n-1)+n.Find f(2): Using the recursive formula for n=2, we get f(2)=-2f(2-1)+2. Substitute f(1)=1 into the equation: f(2)=-2(1)+2.Calculate f(2): Calculate the value of f(2): f(2)=-2*1+2. f(2)=-2+2. f(2)=0.Find f(3): Now that we have f(2)=0, we can use the recursive formula to find f(3). f(3)=-2f(3-1)+3. Substitute f(2)=0 into the equation: f(3)=-2(0)+3.Calculate f(3): Calculate the value of f(3): f(3)=-2*0+3. f(3)=0+3. f(3)=3.

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

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

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Algebra 2

Evaluate exponential functions

Full solution

Q. If

f(1)=1

and

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

then find the value of

f(3)

\newline

Answer:

Given Function and Initial Value: We are given $f(1)=1$ . To find $f(3)$ , we first need to find $f(2)$ using the recursive formula $f(n)=-2f(n-1)+n$ .
Find $f(2)$ : Using the recursive formula for $n=2$ , we get $f(2)=-2f(2-1)+2$ . $\newline$ Substitute $f(1)=1$ into the equation: $f(2)=-2(1)+2$ .
Calculate $f(2)$ : Calculate the value of $f(2)$ : $f(2)=-2\times 1+2$ . $\newline$ $f(2)=-2+2$ . $\newline$ $f(2)=0$ .
Find $f(3)$ : Now that we have $f(2)=0$ , we can use the recursive formula to find $f(3)$ . $f(3)=-2f(3-1)+3$ . Substitute $f(2)=0$ into the equation: $f(3)=-2(0)+3$ .
Calculate $f(3)$ : Calculate the value of $f(3)$ : $f(3)=-2\times 0+3$ . $\newline$ $f(3)=0+3$ . $\newline$ $f(3)=3$ .