Home
Class 11
MATHS
If (m+1)^th ,(n+1)^th and (r+1)^th terms...

If `(m+1)^th` ,`(n+1)^th` and `(r+1)^th` terms in AP are in GP m,n,r are in HP ,show that the ratio of the common difference to the first term of the AP is `(-2/n).`

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

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

If the (m + 1)th, (n + 1)th and (r + 1)th terms of an A.P. are in G.P. and (1)/(m), (1)/(n), (1)/(r ) are in A.P., then find the ratio of the first term of the A.P. to its common difference in terms of n.

If n - th term of an A.P be 2n-4 , then which one of the following is common difference ?

If the P th term of an AP is (3P - 5), then find the common difference and 15th term of this AP.

If the 2nd ,5ht and 9th terms of a non-constant AP are in GP , then the common ratio of this GP is

If the first term of an A.P. is – 18 and its 10th term is zero, then find its common difference.

If an A.P., the sum of 1st n terms is 2n^2 + 3n , then the common difference will

The sum to n terms of an A.P. is n^(2) . Find the common difference.

The sum of n terms of an A.P is n^2 .Find the common difference.

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The sum of the squares of three distinct real numbers, which are in GP...

    Text Solution

    |

  2. Prove that the three successive terms of a GP will form the sides of ...

    Text Solution

    |

  3. If (m+1)^th ,(n+1)^th and (r+1)^th terms in AP are in GP m,n,r are in ...

    Text Solution

    |

  4. If p be the first of n arithmetic means between two numbers and q be t...

    Text Solution

    |

  5. Show that 1^4/13+2^4/3.5+3^4/5.7+.....+n^4/((2n-1)(2n+1))=(n(4n^2+6n+5...

    Text Solution

    |

  6. Solve the following equations for x and y log10xx+1/2log10xx+1/4log10x...

    Text Solution

    |

  7. Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7)...upto infinit...

    Text Solution

    |

  8. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

    Text Solution

    |

  9. If 1,log9(3^(1-x)+2) and log3(4.3^x-1) are in AP , then x is equal to

    Text Solution

    |

  10. If the sum of the first 2n terms of the AP 2,5,8.....is equal to the s...

    Text Solution

    |

  11. If xin R , the number 5^(1+x)+5^(1-x),a/2,25^x+25^-xform an AP , then ...

    Text Solution

    |

  12. If an AP a7=9 and a1a2a7 is least , then common difference is

    Text Solution

    |

  13. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  14. The value of a^(logb(x))=(where, a=0.2,b=sqrt5), x=(1/4+1/8+1/16+........

    Text Solution

    |

  15. If a,b,c are in HP and agtcgt0, then 1/(b-c)-1/(a-b).

    Text Solution

    |

  16. Let the positive numbers a,b,c,d be in AP , Then abc, abd,acd,bcd are

    Text Solution

    |

  17. If a,b,c are in HP , thn the value of (b+a)/(b-a)+(b+c)/(b-c) is

    Text Solution

    |

  18. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

  19. If three positive real number a,b,c are in AP with abc =4 , then the m...

    Text Solution

    |

  20. The sum of 10 terms of the series 0.7+.77+.777+.... is

    Text Solution

    |