If f(1)=8 and f(n)=-2f(n-1)+1 then find the value of f(5). Answer:

Given f(1) = 8: We are given that f(1) = 8. To find f(5), we need to find the values of f(2), f(3), f(4), and then f(5) using the recursive formula f(n) = -2f(n-1) + 1.Find f(2): First, let's find f(2) using the formula with n=2: f(2) = -2f(2-1) + 1 f(2) = -2f(1) + 1 f(2) = -2(8) + 1 f(2) = -16 + 1 f(2) = -15Find f(3): Next, we find f(3) using the formula with n=3: f(3) = -2f(3-1) + 1 f(3) = -2f(2) + 1 f(3) = -2(-15) + 1 f(3) = 30 + 1 f(3) = 31Find f(4): Now, we find f(4) using the formula with n=4: f(4) = -2f(4-1) + 1 f(4) = -2f(3) + 1 f(4) = -2(31) + 1 f(4) = -62 + 1 f(4) = -61Find f(5): Finally, we find f(5) using the formula with n=5: f(5) = -2f(5-1) + 1 f(5) = -2f(4) + 1 f(5) = -2(-61) + 1 f(5) = 122 + 1 f(5) = 123

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If
f(1)=8 and
f(n)=-2f(n-1)+1 then find the value of
f(5).
Answer:

If $f(1)=8$ and $f(n)=-2 f(n-1)+1$ then find the value of $f(5)$ . $\newline$ Answer:

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Full solution

Q. If

f(1)=8

and

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

then find the value of

f(5)

\newline

Answer:

Given $f(1) = 8$ : We are given that $f(1) = 8$ . To find $f(5)$ , we need to find the values of $f(2)$ , $f(3)$ , $f(4)$ , and then $f(5)$ using the recursive formula $f(n) = -2f(n-1) + 1$ .
Find $f(2)$ : First, let's find $f(2)$ using the formula with $n=2$ :
$f(2) = -2f(2-1) + 1$
$f(2) = -2f(1) + 1$
$f(2) = -2(8) + 1$
$f(2) = -16 + 1$
$f(2) = -15$
Find $f(3)$ : Next, we find $f(3)$ using the formula with $n=3$ :
$f(3) = -2f(3-1) + 1$
$f(3) = -2f(2) + 1$
$f(3) = -2(-15) + 1$
$f(3) = 30 + 1$
$f(3) = 31$
Find $f(4)$ : Now, we find $f(4)$ using the formula with $n=4$ :
$f(4) = -2f(4-1) + 1$
$f(4) = -2f(3) + 1$
$f(4) = -2(31) + 1$
$f(4) = -62 + 1$
$f(4) = -61$
Find $f(5)$ : Finally, we find $f(5)$ using the formula with $n=5$ :
$f(5) = -2f(5-1) + 1$
$f(5) = -2f(4) + 1$
$f(5) = -2(-61) + 1$
$f(5) = 122 + 1$
$f(5) = 123$