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If f(5) = 12, what is the value of f(1)

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If f(5) = 12, what is the value of f(1)  [#permalink]

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New post 06 Nov 2017, 11:57
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Difficulty:

  45% (medium)

Question Stats:

66% (01:31) correct 34% (01:53) wrong based on 70 sessions

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f(n+1) = n + \(\frac{f(n)}{2}\)

If f(5) = 12, what is the value of f(1)?

A. 0
B. 64
C. 78
D. 94
E. 98

Source: Experts Global

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If f(5) = 12, what is the value of f(1)  [#permalink]

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New post 06 Nov 2017, 12:11
pushpitkc wrote:
f(n+1) = n + \(\frac{f(n)}{2}\)

If f(5) = 12, what is the value of f(1)?

A. 0
B. 64
C. 78
D. 94
E. 98

Source: Experts Global


\(f(4+1)=4+\frac{f(4)}{2}=12 => f(4)=16\)

\(f(3+1)=3+\frac{f(3)}{2}=16 =>f(3)=26\)

\(f(2+1)=2+\frac{f(2)}{2}=26 => f(2)=48\)

\(f(1+1)=1+\frac{f(1)}{2}=48 =>f(1)=94\)

Option D
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Re: If f(5) = 12, what is the value of f(1)  [#permalink]

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New post 12 Nov 2017, 08:31
pushpitkc wrote:
f(n+1) = n + \(\frac{f(n)}{2}\)

If f(5) = 12, what is the value of f(1)?

A. 0
B. 64
C. 78
D. 94
E. 98


Since f(5) = 12, n = 4 and we have:

f(4 + 1) = 4 + f(4)/2

12 = 4 + f(4)/2

8 = f(4)/2

f(4) = 16

Since we know the value of f(4), we can calculate the value of f(3) as follows:

f(3 + 1) = 3 + f(3)/2

16 = 3 + f(3)/2

13 = f(3)/2

f(3) = 26

Similarly, we can calculate the value of f(2) as follows:

f(2 + 1) = 2 + f(2)/2

26 = 2 + f(2)/2

24 = f(2)/2

f(2) = 48

Finally, we can calculate the value of f(1) as follows:

f(1 + 1) = 1 + f(1)/2

48 = 1 + f(1)/2

47 = f(1)/2

f(1) = 94

Answer: D
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Re: If f(5) = 12, what is the value of f(1) &nbs [#permalink] 12 Nov 2017, 08:31
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