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If the geometic mean between a and b is ...

If the geometic mean between a and b is `(a^(n + 1) + b^(n + 1))/(a^(n) + b^(n))` , then n

A

0

B

`1//2`

C

`-1//2`

D

`1//2`

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. Let a(1), a(2), …., a(10) be in A.P and h(1), h(2),…. , h(10) be I H.P...

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  2. If the arthimetic mean between a and b is (a^(n + 1) + b^(n + 1))/(a^(...

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  3. If the geometic mean between a and b is (a^(n + 1) + b^(n + 1))/(a^(n)...

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  4. If the harmonic mean between a and b is (a^(n + 1) + b^(n - 1))/(a^(n)...

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  5. x,y are two real numbers. If A is half of their sum, G is root of thei...

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  6. If the first and (2n + 1)th terms of an A.P. , G.P. and H.P. are equal...

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  7. If H(1), H(2), ….. H(n) are n harmonic means between a and b (ne a), t...

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  8. The harmonic mean of two numbers is 4 their arithmetic mean is A and g...

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  9. The ratio of the harmonic mean to the geometric mean of two positive n...

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  10. If b + c, c + a , a + b are in A.P then a , b , c are in

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  11. If a^(2), b^(2), c^(2) are in A.P., then (a)/(b + c) , (b)/(c + a), (c...

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  12. IF the roots of (b-c) x^2+ (c-a) x+ (a-b) =0 are equal then ...

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  13. IF the roots of a(b-c)x^2+b (c-a) x+c (a-b)=0 are equal then a, ...

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  14. If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 ...

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  15. If the system of linear equations x+2ay+az=0, x+3by+bz=0,x+4ch+cz=0 ha...

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  16. Let f (x ) be a polynomial function of second degree. If f (1) = f( -1...

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  17. If x gt 1, y gt 1 , z gt 1 are in G.P then (1)/(1 + log x ), (1)/( 1...

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  18. If (a + bx)/(a - bx) = (b + cx)/(b - cx) = (c + dx)/(c - dx)( x ne 0),...

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  19. If a^(x) = b^(y) = c^(z) = d^(t) and a ,b ,c d are in G.P . Then x, y,...

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  20. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

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