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If one geometric mean G and two arithmet...

If one geometric mean `G` and two arithmetic means `A_1a n dA_2` be inserted between two given quantities, prove that `G^2=(2A_1-A_2)(2A_2-A_1)dot`

A

0

B

1

C

`-1.5`

D

`-2.5`

Text Solution

Verified by Experts

The correct Answer is:
B
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MCGROW HILL PUBLICATION-PROGRESSIONS-SOLVED EXAMPLES LEVEL -1 (SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

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  2. If sum of the infinite G.P. p+1+(1)/(p)+(1)/(p^(2))+… (p gt 2) is 49/6...

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  3. lt a1, a2, a3 ....... terms of this A.P., such that a4-a7+a10, then th...

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  4. If (20)^(19)+2(21)(20)^(18)+3(21)^(2)(20)^(17)+….+20(21)^(19)=k(20)^(1...

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  5. Three positive numbers form an increasing GP. If the middle term in th...

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  6. Suppose m arithmeti means are inserted between 1 and 31. If the ratio ...

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  7. In a geometric progression the ratio of the sum of the first 5 terms t...

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  8. If the r^(th) term of a series is 1 + x + x^2 + .......+ x^(r-1) , the...

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  9. Let m be a positive integer, then S=overset(m)underset(k=1)Sigmak((1)/...

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  10. Let f(n)=[(1)/(5)+(3n)/(100)]n, where [x] denotes the greatest integer...

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  11. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

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  12. The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...

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  13. The positive integer n for which 2xx2^2xx+3xx2^3+4xx2^4++nxx2^n=2^(n+1...

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  14. Sum of the series S=1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+........... upt...

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  15. If 1^(2)+2^(2)+3^(2)+…+2009^(2)=(2009)(4019)(335) and (1) (2009) +(2) ...

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  16. If x gt 0, and log(2) + log(2)(sqrt(x)) + log(2) (4sqrt(x)) + log(2) (...

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  17. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

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  18. Let a1, a2, ,a(10) be in A.P. and h1, h2, h(10) be in H.P. If a1=h1=2...

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  19. If a,b,c are in A.P.and a^(2),b^(2),c^(2) are in G.P.such that a lt ...

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  20. Let S1, S2, be squares such that for each ngeq1, the length of a side...

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