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

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Joined: 26 Feb 2016
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If f(5) = 12, what is the value of f(1)  [#permalink]

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06 Nov 2017, 11:57
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Difficulty:

45% (medium)

Question Stats:

68% (02:15) correct 33% (02:05) wrong based on 80 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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Joined: 25 Feb 2013
Posts: 1164
Location: India
GPA: 3.82
If f(5) = 12, what is the value of f(1)  [#permalink]

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06 Nov 2017, 12:11
1
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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Posts: 2812
Re: If f(5) = 12, what is the value of f(1)  [#permalink]

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12 Nov 2017, 08:31
1
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

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

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20 Oct 2019, 02:25
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Re: If f(5) = 12, what is the value of f(1)   [#permalink] 20 Oct 2019, 02:25
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