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IF F(n + 1) = 2F(n) +1/2( WHOLE DIVIDED BY 2) , WHERE n=1,2,3..... AND F(1)=2 , THEN THE VALUE OF F(11)=?

  1. IF F(n + 1) = 2F(n) +1/2( WHOLE DIVIDED BY 2) , WHERE n=1,2,3..... AND F(1)=2 , THEN THE VALUE OF F(11)=?

Grade:Select Grade

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

F(n+1) = \frac{2F(n)+1}{2}
n = 1
F(1+1) = \frac{2F(1)+1}{2}
F(2) = \frac{2(2) + 1}{2} = \frac{5}{2}
F(n+1) = F(n) + \frac{1}{2}
F(n+1) - F(n) = \frac{1}{2}
So it form an AP with a common difference of ½.
2,\frac{5}{2},3,\frac{7}{2},.............
F(11) = F(1) + 10d
F(11) = 2 + 10.\frac{1}{2}
F(11) = 2 + 5 = 7

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