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Differential Calculus> IF F(n + 1) = 2F(n) +1/2( WHOLE DIVIDED B...

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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)=?

Bharat Makkar , 10 Years ago

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1 Answers

Jitender Singh

Last Activity: 10 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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