Home
Class 12
MATHS
If a+c = 2b and ab + cd + ad = 3bc, prov...

If a+c = 2b and ab + cd + ad = 3bc, prove that the four numbers a, b, c, d are in A.P. `(b != 0)`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 B (Long Answer Type Questions)|52 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 C (Multiple Choice Type Questions)|14 Videos

  • SEQUENCE AND SERIES

    CHHAYA PUBLICATION|Exercise Exercise 9 B (Very Short Answer Type Questions)|18 Videos

  • SECOND ORDER DERIVATIVE

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion-Reason type)|2 Videos

  • SET THEORY

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

If a+c = 2b and 2/c= 1/b+1/d then prove that a:b = c:d.

Let a,b,c,d, be four quantities such that a+c=2 b and ab+cd+ad=3bc(b ne 0) . Prove that a,b,c and d are in A.P.

If a, b, c are in H.P., prove that, a(b+c), b(c+a), c(a+b) are in A.P.

a,b and c are in A.P. Prove that b+c , c+a and a+b are in A.P.

If a , b , c , are three unequal number such that a , b ,c are in A.P and (b-a),(c-b) , a are in G.P then find a: b: c .

If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

If a : b = c : d , then prove that the - proportional of (a^(2) + c^(2)) " and " (b^(2) + d^(2)) " is " (ab + cd) .

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.

If (b+c-a)/a ,(c+a-b)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ,1/c are also in A.P.

CHHAYA PUBLICATION-SEQUENCE AND SERIES-Exercise 9 B (Short Answer Type Questions)
  1. If a, b, c are In A.P., then show that, (1)/(b c), (1)/(c a), (1)/(a...

    Text Solution

    |

  2. If the pth , qth and rth terms of an A.P. be P, Q and R respectively t...

    Text Solution

    |

  3. If (b+c)/(a), (c+a)/(b), (a+b)/(c ) are in A.P. show that (1)/(a), (1)...

    Text Solution

    |

  4. Let a(a != 0) is a fixed real number and (a-x)/(p x) = (a-y)/(qy) = (a...

    Text Solution

    |

  5. If a+c = 2b and ab + cd + ad = 3bc, prove that the four numbers a, b, ...

    Text Solution

    |

  6. Find the least value of n for which the sum of the series 20 + 28 + 36...

    Text Solution

    |

  7. The nth term of a series in A.P. is an + b. Find the sum of the series...

    Text Solution

    |

  8. Find the sum of the series 1^(2) - 2^(2) - 3^(2) - 4^(2) + 5^(2) - 6^(...

    Text Solution

    |

  9. The perpendicular of a right angled triangle is 9 cm and the three sid...

    Text Solution

    |

  10. If the xth term of an A.P. is (1)/(y) and its yth term is (1)/(x) then...

    Text Solution

    |

  11. An A.P. consists of n terms. If the sum of its first three terms is x ...

    Text Solution

    |

  12. If S be the sum of first (2n+1) terms of an A.P and the sum of terms i...

    Text Solution

    |

  13. The sum of first p terms of an A.P. is (p^(2))/(n) and the sum of its ...

    Text Solution

    |

  14. If the A.M. of (1)/(b-a) and (1)/(b-c) is (1)/(2(b-x)), then show that...

    Text Solution

    |

  15. A farmer undertakes to pay off a debt of Rs. 2700 by monthly instalmen...

    Text Solution

    |

  16. A person pays Rs.975 in monthly instalments, each instalment is less t...

    Text Solution

    |

  17. If 1 paisa is saved today, 2 paise next day, 3 paise succeeding day an...

    Text Solution

    |

  18. The cost of sinking a tubewell is 25 paise for the first metre and an ...

    Text Solution

    |

  19. The rate of monthly salary of an office assistant is increased annuall...

    Text Solution

    |

  20. The angles of a polygon are in A.P. lying common difference 5^(@). If ...

    Text Solution

    |