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06 Nov 2017, 11:57
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D
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Difficulty:
45%
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Question Stats:
70% (02:18) correct
30%
(02:08)
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based on 240
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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
If f(5) = 12, what is the value of f(1)?
A. 0
B. 64
C. 78
D. 94
E. 98
Source: Experts Global
06 Nov 2017, 12:11
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pushpitkc
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
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
12 Nov 2017, 08:31
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pushpitkc
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
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
