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

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BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2094
Location: India
GPA: 3.12
If f(5) = 12, what is the value of f(1) [#permalink]

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06 Nov 2017, 10:57
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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
[Reveal] Spoiler: OA

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 948
Location: India
GPA: 3.82
If f(5) = 12, what is the value of f(1) [#permalink]

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06 Nov 2017, 11:11
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

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

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

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

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

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

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12 Nov 2017, 07:31
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

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Re: If f(5) = 12, what is the value of f(1)   [#permalink] 12 Nov 2017, 07:31
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