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Suppose that F(n +1) =( 2f(n)+1)/2 for ...

Suppose that `F(n +1) =( 2f(n)+1)/2` for n = 1, 2, 3,.....and f(1)= 2 Then F(101) equals = ?

A

50

B

52

C

54

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given,
`F(n+1)=(2F(n)+1)/2`
`rArrF(n+1)-F(n)=1//2`
Hence, the given series is an A.P. with common difference 1/2 and first term being 2. F(101) is 101st term of A.P. given by
2+(101-1)(1/2)=52
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CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
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  6. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

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  7. If the sum of m terms of an A.P. is same as the sum of its n terms, th...

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  8. If Sn, denotes the sum of n terms of an A.P., then S(n+3)-3S(n+2)+3S(n...

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  9. The first term of an A.P. is a and the sum of first p terms is zero, s...

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  11. The number of terms of an A.P. is even, the sum of odd terms is 24, of...

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  12. The number of terms of an A.P. is even, the sum of odd terms is 24, of...

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  13. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

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  14. If a1,a2,a3….a(2n+1) are in A.P then (a(2n+1)-a1)/(a(2n+1)+a1)+(a2n-...

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  15. If a(1), a(2), …..,a(n) are in A.P. with common difference d ne 0, the...

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  16. ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n p...

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  17. If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

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  18. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4a n dt2+...

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