If f(1)=10 and f(n)=-5f(n-1)-n then find the value of f(3). Answer:

Find f(2): Use the given recursive formula to find f(2). We know that f(1) = 10. To find f(2), we use the formula f(n) = -5f(n-1) - n with n = 2. f(2) = -5f(2-1) - 2 f(2) = -5f(1) - 2 f(2) = -5(10) - 2 f(2) = -50 - 2 f(2) = -52Calculate f(3): Use the value of f(2) to find f(3). Now that we have f(2) = -52, we can use the formula f(n) = -5f(n-1) - n with n = 3. f(3) = -5f(3-1) - 3 f(3) = -5f(2) - 3 f(3) = -5(-52) - 3 f(3) = 260 - 3 f(3) = 257

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If
f(1)=10 and
f(n)=-5f(n-1)-n then find the value of
f(3).
Answer:

If $f(1)=10$ and $f(n)=-5 f(n-1)-n$ then find the value of $f(3)$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=10

and

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

then find the value of

f(3)

\newline

Answer:

Find $f(2)$ : Use the given recursive formula to find $f(2)$ . We know that $f(1) = 10$ . To find $f(2)$ , we use the formula $f(n) = -5f(n-1) - n$ with $n = 2$ . $f(2) = -5f(2-1) - 2$ $f(2) = -5f(1) - 2$ $f(2) = -5(10) - 2$ $f(2) = -50 - 2$ $f(2)$ $0$
Calculate $f(3)$ : Use the value of $f(2)$ to find $f(3)$ . $\newline$ Now that we have $f(2) = -52$ , we can use the formula $f(n) = -5f(n-1) - n$ with $n = 3$ . $\newline$ $f(3) = -5f(3-1) - 3$ $\newline$ $f(3) = -5f(2) - 3$ $\newline$ $f(3) = -5(-52) - 3$ $\newline$ $f(3) = 260 - 3$ $\newline$ $f(2)$ $0$