Home
Class 12
MATHS
if (m+1)th, (n+1)th and (r+1)th term of ...

if `(m+1)th, (n+1)th and (r+1)th` term of an AP are in GP.and m, n and r in HP. . find the ratio of first term of A.P to its common difference

A

`-n/2`

B

`-m/2`

C

r

D

`-(mr)/(m+r)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION & SERIES

    FIITJEE|Exercise COMPREHENSIONS -I|3 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise COMPREHENSIONS -II|2 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I|50 Videos

  • PROBABILITY

    FIITJEE|Exercise Exercise 7|2 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

The pth, (2p)th and (4p)th terms of an AP, are in GP, then find the common ratio of GP.

If n^(th) term of A.P is 2n+3, then common difference is

The 1 st,4 th and 13 th terms of AP are in G.P. The first term is 3. Find the A.P.

If the 5th and 12th terms of an A.P. are 14 and 35 respectively, find the first term and the common difference.

If the n^(th) term of an A.P is (5n-2) ,find its Common difference

If m^(th) n^(th) and o^(th) term of an A.P. are n, o and m. Find common difference d.

If m^(th) n^(th) and o^(th) term of an A.P.are n ,o and m .Find common difference d.

The first term of an A.P. is 5 and its common difference is -3 . Find the 11th term of an A.P.

If the nth term of an A.P. is 4n-1 , find the 30th term and the sum of first 30 terms.

FIITJEE-PROGRESSION & SERIES -ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II
  1. In a G.P. the product of the first four terms is 4 and the second ter...

    Text Solution

    |

  2. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

    Text Solution

    |

  3. If three unequal positive real numbers a, b, c are in G.P. and b-c, c-...

    Text Solution

    |

  4. For any three unequal numbers a,b and c (a-b)/(b-c) equals to

    Text Solution

    |

  5. The numbers 1, 4, 16 can be three terms (not necessarily consecutive) ...

    Text Solution

    |

  6. Let a and b be two positive unequal numbers , then (a^(n+1)+b^(n+1))/(...

    Text Solution

    |

  7. Let a1, a2, a3, ,an be in G.P. such that 3a1+7a2+3a3-4a5=0. Then comm...

    Text Solution

    |

  8. If x,y,z are positive numbers in A.P., then

    Text Solution

    |

  9. The sequences {x(n)} is defined by x(k+1)=x(k)^(2)+x(k) and x(1) =1/...

    Text Solution

    |

  10. If a,b,c are in G.P and a,p,q are in A.P such that 2a, b+p, c +q are...

    Text Solution

    |

  11. If a,b,c three unequal positive quantities in H.P .then

    Text Solution

    |

  12. If underset(k=1)overset(n)sum(underset(m=1)overset(k)summ^(2))=an^(4)+...

    Text Solution

    |

  13. For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) ...

    Text Solution

    |

  14. Let x(1),x(2),x(3) bet the roots of equation x^(3) - x^(2) +betax + ga...

    Text Solution

    |

  15. The value of sum(r=1)^n1/(sqrt(a+r x)+sqrt(a+(r-1)x)) is -

    Text Solution

    |

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

    Text Solution

    |

  17. If a, b, c, d are distinct integers in A. P. Such that d=a^2+b^2+c^2, ...

    Text Solution

    |

  18. If a,b,c, are in A.P., b,c,d are in G.P. and c,d,e, are in H.P., then ...

    Text Solution

    |

  19. if the equation x^(4)-4x^(3)+ax^(2)+bx+1=0 has four positive roots, th...

    Text Solution

    |

  20. If a,b,and c are three terms of an A.P such that a != b then (b-c)/...

    Text Solution

    |