Home
Class 11
MATHS
a1,a2,a3.....an are in H.P. (a(1))/(a(2)...

a1,a2,a3.....an are in H.P. `(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_(n-1))` are in

A

A.P.

B

G.P.

C

H.P.

D

A.G.P.

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that `a_(1),a_(2), . . .,a_(n)` are in H.P.
`:." "(1)/(a_(1)),(1)/(a_(2)),(1)/(a_(3)), . . .,(1)/(a_(n))` are in AP.
`rArr" "(a_(1)+a_(2)+a_(3)+ . . . +a_(n))/(a_(1)),(a_(1)+a_(2)+a_(3)+ . . . +a_(n))/(a_(2)), . . . ,(a_(1)+a_(2)+ . . .+a_(n))/(a_(n))` are in A.P.
`rArr" "1+(a_(2)+a_(3)+ . . .+a_(n))/(a_(1)),1+(a_(1)+a_(3)+ . . .+a_(n))/(a_(2)), . . . ,(a_(1)+a_(2)+ . . .+a_(n-1))/(a_(n))+1` are in A.P.
`rArr" "(a_(2)+a_(3)+ . . .+a_(n))/(a_(1)),(a_(1)+a_(3)+ . . . +a_(n))/(a_(2)), . . .,(a_(1)+a_(2)+ . . .+a_(n-1))/(a_(n))` are in A.P.
`rArr" "(a_(1))/(a_(2)+a_(3)+ . . . .+a_(n)),(a_(2))/(a_(1)+a_(3)+ . . ..+a_(n)), . . .,(a_(n))/(a_(1)+a_(2)+ . . . +a_(n-1))` are in H.P.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|80 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

If (a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

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 find (a_(6))/(a_(21)) .

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

If a_1, a_2, a_3, ,a_(2n+1) are in A.P., then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_(2n)-a_2)/(a_(2n)+a_2)++(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to a. (n(n+1))/2xx(a_2-a_1)/(a_(n+1)) b. (n(n+1))/2 c. (n+1)(a_2-a_1) d. none of these

If a_(1), a_(2), . . . , a_(n) is a sequence of non-zero number which are in A.P., show that (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+. . . + (1)/(a_(n)a_(1))= (2)/(a_(1) + a_(n)) [(1)/(a_(1))+(1)/(a_(2))+. . . +(1)/(a_(n))]

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. a1,a2,a3.....an are in H.P. (a(1))/(a(2)+a(3)+ . . .+a(n)),(a(2))/(a(1...

    Text Solution

    |

  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

    Text Solution

    |

  3. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

    Text Solution

    |

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

    Text Solution

    |

  5. If the (m+1)t h ,(n+1)t h ,a n d(r+1)t h terms of an A.P., are in G.P....

    Text Solution

    |

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

    Text Solution

    |

  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

    Text Solution

    |

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

    Text Solution

    |

  11. If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero nu...

    Text Solution

    |

  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

    Text Solution

    |

  13. The sides of a right angled triangle are in A.P., then they are in the...

    Text Solution

    |

  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

    Text Solution

    |

  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

    Text Solution

    |

  16. If three numbers are in G.P., then the numbers obtained by adding the ...

    Text Solution

    |

  17. If p ,q ,r are in A.P., show that the pth, qth and rth terms of any G....

    Text Solution

    |

  18. Let a,b,c be three positive prime number. The progrrssion in which sqr...

    Text Solution

    |

  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a...

    Text Solution

    |

  20. If three numbers are in H.P., then the numbers obtained by subtracting...

    Text Solution

    |

  21. The first three of four given numbers are in G.P. and their last three...

    Text Solution

    |