Home
Class 12
MATHS
If a1, a2, a3, an are in H.P. and f(k)=...

If `a_1, a_2, a_3, a_n` are in H.P. and `f(k)=(sum_(r=1)^n a_r)-a_k ,t h e n` `(a_1)/(f(1)),(a_2)/(f(2)),(a_3)/(f(3)), ,(a_n)/(f(n)),` are in a. A.P b. G.P. c. H.P. d. none of these

A

A.P

B

GP.

C

H.P.

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-2: CONCEPT APPLICATOR|30 Videos

  • SETS

    DISHA PUBLICATION|Exercise EXERCISE-2 : CONCEPT APPLICATOR|30 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),...a_(n) are in H.P.and f(k)=(sum_(r=1)^(n)a_(r))-a_(k), then (a_(1))/(f(1)),(a_(2))/(f(2)),(a_(3))/(f(3)),...(a_(n))/(f(n)), are in a.A.P b.G.P. C.H.P.d.none of these

If a_1,a_2, a_3………. are in H.P. and f(k) =sum_(r=1)^n a_r-a_k, the a_1/(f(1)), a_2/(f(2)), a_3/(f(3)), …….., a_n/(f(n)) are in (A) A.P. (B) G.P (C) H.P. (D) none of these

If a_1,a_2,a_3……..a_n are in H.P. and f(k) = sum_(r=1)^na_r-a_k then (f(1))/a_1, (f(2))/a_3 ….f(n)/a_n are (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a_1,a_2,……….,a_(n+1) are in A.P. prove that sum_(k=0)^n ^nC_k.a_(k+1)=2^(n-1)(a_1+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

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

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_n)/(a_1+a_2+….+a_(n-1)) are in

We know that, if a_1, a_2, ..., a_n are in H.P. then 1/a_1,1/a_2,.....,1/a_n are in A.P. and vice versa. If a_1, a_2, ..., a_n are in A.P. with common difference d, then for any b (>0), the numbers b^(a_1),b^(a_2),b^9a_3),........,b^(a_n) are in G.P. with common ratio b^d. If a_1, a_2, ..., a_n are positive and in G.P. with common ration, then for any base b (b> 0), log_b a_1 , log_b a_2,...., log_b a_n are in A.P. with common difference logor.If x, y, z are respectively the pth, qth and the rth terms of an A.P., as well as of a G.P., then x^(z-x),z^(x-y) is equal to

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

DISHA PUBLICATION-SEQUENCES AND SERIES -EXERCISE -1 : Concept Builder
  1. If 1/1^4+1/2^4+1/3^4+...+oo=pi^4/90, then 1/1^4+1/3^4+1/5^4+...+oo=

    Text Solution

    |

  2. If x, y and z are pth, gth and rth terms respectively of an A.P and al...

    Text Solution

    |

  3. The AM, HM and GM between two number are (144)/(15), 15 and 12, but no...

    Text Solution

    |

  4. If a1, a2, a3, an are in H.P. and f(k)=(sum(r=1)^n ar)-ak ,t h e n (a...

    Text Solution

    |

  5. If the p^(th), q^(th) and r^(th) terms of a GP. Are again in G.P., the...

    Text Solution

    |

  6. If x gt 0, (x^(n))/(1+x+x^(2)+...+x^(2n)) is

    Text Solution

    |

  7. If a + b + c = 3 and a > 0, b>0,c>0 the greatest value of a^2b^3c^2

    Text Solution

    |

  8. If 1/(b-a)+1/(b-c)=1/a+1/c , then a,b,c are in (A) AP (B) GP (C) ...

    Text Solution

    |

  9. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  10. If A and G be the AM and GM between two positive no.'s ; then the numb...

    Text Solution

    |

  11. Consider the sequence of numbers 121, 12321, 1234321,... Each term in ...

    Text Solution

    |

  12. The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is 50(1-i) b. 2...

    Text Solution

    |

  13. In a geometric progression with first term a and common ratio r, what ...

    Text Solution

    |

  14. Find the sum of n terms of the series 1+4/5+7/(5^2)+10+5^3+dot

    Text Solution

    |

  15. If the sum to infinty of the series , 1+4x+7x^(2)+10x^(3)+…., is (35)/...

    Text Solution

    |

  16. the sum3/1^2+5/(1^2+2^2)+7/(1^2+2^2+3^2)+....... upto 11 terms

    Text Solution

    |

  17. The sum of the infinite series (1)/(2) ((1)/(3) + (1)/(4)) - (1)/(4)...

    Text Solution

    |

  18. The sum of the series : (2)^(2) + 2(4)^(2) + 3(6)^(2)+.... Upon 10 ter...

    Text Solution

    |

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

    Text Solution

    |

  20. For a positive integer n let a(n)=1+1/2+1/3+1/4+1/((2^n)-1)dot Then a(...

    Text Solution

    |