Home
Class 11
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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 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 the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, find the first' term and the common difference.

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

If 5th and 6th terms of an A.P. are respectively 6 and 5, find the 11th term of the A.P.

If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

The 4th and 7th terms of a G.P. are 1/(27)a n d1/(729) respectively. Find the sum of n terms of the G.P.

The 25th term of an A.P. exceeds its 9th term by 16. Find its common difference.

If mth term of an AP is 1/n and its nth term is 1/m , then show that its (mn)th term is 1

If mth term of an AP is 1/n and its nth term is 1/m , then show that its (mn)th term is 1

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If the pth term of an A.P. is q and the qth term is p , then find its ...

    Text Solution

    |

  2. Find the product of three geometric means between 4 and 1/4.

    Text Solution

    |

  3. 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

    |

  4. Insert four G.M.’s between 2 and 486.

    Text Solution

    |

  5. Find the sum 1^2+(1^2+2^2)+(1^2+2^2+3^2)+ up to 22nd term.

    Text Solution

    |

  6. If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G...

    Text Solution

    |

  7. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

    Text Solution

    |

  8. The sum of infinite number of terms in G.P. is 20 and the sum of their...

    Text Solution

    |

  9. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) ...

    Text Solution

    |

  10. Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

    Text Solution

    |

  11. Three numbers are in G.P. whose sum is 70. If the extremes be each mul...

    Text Solution

    |

  12. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+o...

    Text Solution

    |

  13. Find the sum 1+4+13+40+121+dot

    Text Solution

    |

  14. If each term of an infinite G.P. is twice the sum of the terms foll...

    Text Solution

    |

  15. The sum to n terms of series 1+(1+1/2+1/(2^2))+(1+1/2+1/(2^2)+1/(2^3))...

    Text Solution

    |

  16. Find the sum of the following series: (sqrt(2)+1)+1(sqrt(2)-1)+..........

    Text Solution

    |

  17. If the set of natural numbers is partitioned into subsets S1={1},S2={2...

    Text Solution

    |

  18. If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x ,...

    Text Solution

    |

  19. If the sum of the squares of the first n natural numbers exceeds theri...

    Text Solution

    |

  20. If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N suc...

    Text Solution

    |