If f(1)=7 and f(n+1)=-3f(n)-4 then find the value of f(4) Answer:

Find f(2): Use the given recursive formula to find f(2). We know that f(1) = 7. The recursive formula is f(n+1) = -3f(n) - 4. Substitute n = 1 into the formula to find f(2). f(2) = -3f(1) - 4 f(2) = -3(7) - 4 f(2) = -21 - 4 f(2) = -25Find f(3): Use the recursive formula to find f(3). We now know that f(2) = -25. Substitute n = 2 into the formula to find f(3). f(3) = -3f(2) - 4 f(3) = -3(-25) - 4 f(3) = 75 - 4 f(3) = 71Find f(4): Use the recursive formula to find f(4). We now know that f(3) = 71. Substitute n = 3 into the formula to find f(4). f(4) = -3f(3) - 4 f(4) = -3(71) - 4 f(4) = -213 - 4 f(4) = -217

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If
f(1)=7 and
f(n+1)=-3f(n)-4 then find the value of
f(4)
Answer:

If $f(1)=7$ and $f(n+1)=-3 f(n)-4$ then find the value of $f(4)$ $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=7

and

f(n+1)=-3 f(n)-4

then find the value of

f(4)

\newline

Answer:

Find $f(2)$ : Use the given recursive formula to find $f(2)$ . We know that $f(1) = 7$ . The recursive formula is $f(n+1) = -3f(n) - 4$ . Substitute $n = 1$ into the formula to find $f(2)$ . $f(2) = -3f(1) - 4$ $f(2) = -3(7) - 4$ $f(2) = -21 - 4$ $f(2) = -25$
Find $f(3)$ : Use the recursive formula to find $f(3)$ . We now know that $f(2) = -25$ . Substitute $n = 2$ into the formula to find $f(3)$ . $f(3) = -3f(2) - 4$ $f(3) = -3(-25) - 4$ $f(3) = 75 - 4$ $f(3) = 71$
Find $f(4)$ : Use the recursive formula to find $f(4)$ . We now know that $f(3) = 71$ . Substitute $n = 3$ into the formula to find $f(4)$ . $f(4) = -3f(3) - 4$ $f(4) = -3(71) - 4$ $f(4) = -213 - 4$ $f(4) = -217$