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If a ,a1, a2, a3, a(2n),b are in A.P. a...

If `a ,a_1, a_2, a_3, a_(2n),b` are in A.P. and `a ,g_1,g_2,g_3, ,g_(2n),b` . are in G.P. and `h` s the H.M. of `aa n db ,` then prove that `(a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h`

A

`(2n)/(H)`

B

2nH

C

nH

D

`(n)/(H)`

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The correct Answer is:
A
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS)
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  2. If first and (2n−1)^(th) terms of an A.P., G.P. and H.P. are equal a...

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  3. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

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  4. Given that n arithmetic means are inserted between two sets of numbers...

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  5. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

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  6. Two A.M.'s A(1) and A(2), two G.M.'s G(1) and G(2) and two H.M's H(1) ...

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  7. If A is the arithmetic mean and p and q be two geometric means between...

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  8. If one G.M., G and two A.M.\'s p and q be inserted between two given q...

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  9. If a is the A.M. of ba n dc and the two geometric mean are G1a n dG2, ...

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  10. If p, q, r are + ive, then the minimum value of p^(log q - log r) + q^...

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  11. (i) The value of x + y + z is 15. If a, x, y, z, b are in AP while the...

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  12. If a,b,c,d are in H.P., then ab+bc+cd is equal to

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  13. If a(a), a (2), a (3),…., a(n) are in H.P. and f (k)=sum (r =1) ^(n) a...

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  14. If A, G & H are respectively te A.M., G.M. & H.M. of three positive nu...

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  15. In an H.P., T(p) = q (p + q), T(q) = p (p + q), then p and q are the r...

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  16. If four positive numbers a, b, c, d are in H.P. then which one of the ...

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  17. The A.M., G.M. and H.M. between two positive numbers a and b are equal...

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  18. The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...

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  19. If 2(y-a) is the harmonic mean between y-x and y-z then x-a, y—a and z...

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  20. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

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