If f(1)=1 and f(n+1)=-5f(n)-4 then find the value of f(5). Answer:

Given initial condition: We are given the initial condition f(1) = 1 and the recursive formula f(n+1) = -5f(n) - 4. To find f(5), we need to find the values of f(2), f(3), and f(4) first, using the recursive formula.Find f(2): Using the recursive formula, let's find f(2): f(2) = -5f(1) - 4 f(2) = -5(1) - 4 f(2) = -5 - 4 f(2) = -9Find f(3): Now, let's find f(3): f(3) = -5f(2) - 4 f(3) = -5(-9) - 4 f(3) = 45 - 4 f(3) = 41Find f(4): Next, we find f(4): f(4) = -5f(3) - 4 f(4) = -5(41) - 4 f(4) = -205 - 4 f(4) = -209Find f(5): Finally, we find f(5): f(5) = -5f(4) - 4 f(5) = -5(-209) - 4 f(5) = 1045 - 4 f(5) = 1041

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If
f(1)=1 and
f(n+1)=-5f(n)-4 then find the value of
f(5).
Answer:

If $f(1)=1$ and $f(n+1)=-5 f(n)-4$ then find the value of $f(5)$ . $\newline$ Answer:

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Full solution

Q. If

f(1)=1

and

f(n+1)=-5 f(n)-4

then find the value of

f(5)

\newline

Answer:

Given initial condition: We are given the initial condition $f(1) = 1$ and the recursive formula $f(n+1) = -5f(n) - 4$ . To find $f(5)$ , we need to find the values of $f(2)$ , $f(3)$ , and $f(4)$ first, using the recursive formula.
Find $f(2)$ : Using the recursive formula, let's find $f(2)$ :
$f(2) = -5f(1) - 4$
$f(2) = -5(1) - 4$
$f(2) = -5 - 4$
$f(2) = -9$
Find $f(3)$ : Now, let's find $f(3)$ :
$f(3) = -5f(2) - 4$
$f(3) = -5(-9) - 4$
$f(3) = 45 - 4$
$f(3) = 41$
Find $f(4)$ : Next, we find $f(4)$ :
$f(4) = -5f(3) - 4$
$f(4) = -5(41) - 4$
$f(4) = -205 - 4$
$f(4) = -209$
Find $f(5)$ : Finally, we find $f(5)$ :
$f(5) = -5f(4) - 4$
$f(5) = -5(-209) - 4$
$f(5) = 1045 - 4$
$f(5) = 1041$