Home
Class 12
MATHS
If a(1), a(2),…a(n) are in H.P. then a(1...

If `a_(1), a_(2),…a_(n)` are in H.P. then `a_(1).a_(2) + a_(2).a_(3) + a_(3).a_(4) + …+ a_(n-1) .a_(n)`=

A

`na_(1)a_(n)`

B

`(n -1) a_(1)a_(n)`

C

`n(a_(1) - a_(n))`

D

`(n - 1) (a_(1) - a_(n))`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|49 Videos

  • SETS ( APPENDIX - 1)

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE|70 Videos

Similar Questions

Explore conceptually related problems

If a_(1), a_(2),….a_(n) are in H.P then (a_(1))/(a_(2) + a_(3) + …+ a_(n)), (a_(2))/(a_(1) + a_(3) + …+ a_(n)), (a_(3))/(a_(1) + a_(2) + a_(4)…+ a_(n)) ….(a_(n))/(a_(1) + a_(2) + a_(3) + ….a_(n-1))

If a_(1),a_(2),a_(3),………. are in A.P. such that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225, then a_(1) + a_(2) + a_(3) + …… a_(23) + a_(24) =

If a_(1), a_(2) …… a_(n) are in A.P then (sqrt(a_(1)) + sqrt(a_(n)))/( sqrt(a_(1)) + sqrt(a_(2))) + (sqrt(a_(1)) + sqrt(a_(n)))/(sqrt(a_(2)) + sqrt(a_(3))) + ….. + (sqrt( a_(1)) + sqrt(a_(n)))/( sqrt(a_(n - 1)) + sqrt(a_(n))) =

Let a_(1), a_(2), a_(3) ….. be terms of an A.P. If (a_(1) + a_(2) + …..a_(p))/(a_(1) + a_(2) + …..a_(q)) = (p^(2))/(q^(2)) (p ne q) then (a_(6))/(a_(21))=

Let a_(1), a_(2), …., a_(10) be in A.P and h_(1), h_(2),…. , h_(10) be I H.P if a_(1) = h_(1) = 2 and a_(10) = h_(10) = 3, then a_(4) h_(7) is

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

a_(n) = 2^(n), a_(5) = ………

Let a_(1), a_(2) ….a_(10) be A.P and h_(1), h_(2)…h_(10) be in H.P. If a_(1)=h_(1)=2 and a_(10)= h_(10)=3 the a_(3)h_(8) =

DIPTI PUBLICATION ( AP EAMET)-SEQUENCES AND SERIES -EXERCISE
  1. If mth terms of H.P is n and nth term is m, then (m + n)th term is

    Text Solution

    |

  2. If a,b,c are in H.P and ab + bc ca = 15, then ca =

    Text Solution

    |

  3. If a(1), a(2),…a(n) are in H.P. then a(1).a(2) + a(2).a(3) + a(3).a(4)...

    Text Solution

    |

  4. The cotangents of the angles pi//3, pi//4, pi//6 are in

    Text Solution

    |

  5. If three are four harmonic means between 1/12, 1/42, then the third h...

    Text Solution

    |

  6. Two harmonic means between 1/2, 4/17 are

    Text Solution

    |

  7. H(1),H(2) are 2 H.M.'s between a,b then (H(1) + H(2))/(H(1).H(2)) =

    Text Solution

    |

  8. Let a(1), a(2), …., a(10) be in A.P and h(1), h(2),…. , h(10) be I H.P...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |