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In a sequence of (4n + 1) terms the firs...

In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP whose common difference is 2, and the last (2n + 1) terms are in GP whose common ratio is 0.5. If the middle terms of the AP and GP are equal, then the middle term of the sequence is

A

`(n.2^(n + 1))/(2^(n) - 1)`

B

`(n.2^(n + 1))/(2^(2n) - 1)`

C

`n.2^(n)`

D

none

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The correct Answer is:
A
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 2 (MULTIPLE CHOICE QUESTIONS)
  1. A. G.P. consists of an even number of terms. If the sum of all the ...

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  2. A.G.P. consists of 2n terms. If the sum of the terms occupying the odd...

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  3. In a sequence of (4n + 1) terms the first (2n + 1) terms are in AP wh...

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  4. If the sum of n terms of a G.P. is 3(3^(n+1))/(4^(2n)) , then find the...

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  5. Three numbers form an increasing G.P. If the middle number is doubled,...

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  6. Let f(x)=2x+1. Then the number of real number of real values of x for ...

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  7. If a, b and c be three distinct real number in G.P. and a + b + c = xb...

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  8. If a, b, c be in G.P., then the expression a^(2)b^(2)c^(2) ((1)/(a^(3)...

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  9. How many terms of the series 1, 4, 16,… must be taken to have their su...

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  10. The sum of n terms of the series 1 + (1)/(2) + (1)/(2^(2)) +… is less ...

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  11. The minimum value of n such that 1 + 3 + 3^(2) +...+ 3^(n) gt 1000 is

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  12. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  13. Let S1 , S2 , …. Be squares such that for each n ge 1 the length of a...

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  14. If A and G be the A .M and G.M between two positive numbers, then the ...

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  15. If the A.M. and G.M. between two numbers are in the ratio m.n., then w...

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  16. If S = (2)/(3) + (8)/(9) + (26)/(27) + (30)/(81)+….+n terms, then the ...

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  17. Sum of n terms of the series (1)/(3) + (5)/(9) + (19)/(27) + (65)/(81)...

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  18. 8 + 88 + 888 +…n terms =

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  19. underset("n digits")((666…6)^(2)) + underset("n digits")((888…8)) is e...

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  20. The value of sum sum(n=1)^(13) ( i^(n) + i^(n+1)) where i= sqrt( -1) ,...

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