Home
Class 11
MATHS
If a, b, c, d are in G.P., prove that a^...

If a, b, c, d are in G.P., prove that `a^(2) - b^(2), b^(2)-c^(2), c^(2)-d^(2)` are also in G.P.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    ICSE|Exercise EXERCISE 14 (a) |13 Videos

  • SEQUENCE AND SERIES

    ICSE|Exercise EXERCISE 14 (b) |22 Videos

  • SELF ASSESSMENT PAPER 5

    ICSE|Exercise SECTION C|11 Videos

  • SEQUENCES AND SERIES

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS|34 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in A.P., prove that a^(2)(b+c),b^(2)(c+a),c^(2)(a+b)" are also in A.P."

If a ,b,c , d are in G.P. prove that (a-d)^(2) = (b -c)^(2)+(c-a)^(2) + (d-b)^(2)

If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) are in G.P. (a^2-b^2),(b^2-c^2),(c^2-d^2) are in G.P. 1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2) are in G.P.

If a, b, c , d are in G.P. , then shown that (i) (a + b)^(2) , (b +c)^(2), (c + d)^(2) are in G.P. (ii) (1)/(a^(2) + b^(2)), (1)/(b^(2) +c^(2)), (1)/(c^(2) + d^(2)) are in G.P.

If a ,b ,c are in G.P., prove that: a(b^2+c^2)=c(a^2+b^2)

If a, b, c are in G. P. , prove that a^2+ b^2, ab + bc, b^2 +c^2 are also in G.P

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

If a, b, c, d are in G. P., show that they are also in G. P. a^(2)+b^(2),b^(2) +c^(2), c^(2)+d^(2)

If a, b, c are in G.P. show that the are also in G.P. a^(2),b^(2),c^(2)

ICSE-SEQUENCE AND SERIES -CHAPTER TEST
  1. If a, b, c, d are in G.P., prove that a^(2) - b^(2), b^(2)-c^(2), c^(2...

    Text Solution

    |

  2. Write down the first five terms of the sequence, whose nth term is (-1...

    Text Solution

    |

  3. If the 3rd and the 6th terms of an A.P. are 7 and 13 respectively, fin...

    Text Solution

    |

  4. Find the sum of all natural numbers between 100 and 1000 which are mul...

    Text Solution

    |

  5. How many terms of the A.P., -6,(-11)/(2),-5 ... are needed to give the...

    Text Solution

    |

  6. Determine the sum of the first 35 terms of an A.P. if a(2), = 2 and a(...

    Text Solution

    |

  7. If the first term of an A.P. is 2 and the sum of first five terms is e...

    Text Solution

    |

  8. Insert 3 arithmetic means between 2 and 10.

    Text Solution

    |

  9. Find 12th term of a G.P. whose 8th term is 192 and the common ratio is...

    Text Solution

    |

  10. The first term of a G.P. is 1. The sum of the third and fifth terms is...

    Text Solution

    |

  11. The sum of first three terms of a G.P. is (39)/(10) and their product ...

    Text Solution

    |

  12. The sum of some terms of a G.P. is 315 whose first term and the common...

    Text Solution

    |

  13. Find the sum of the series 0.6 +0.66 +0.666+ ... to the n terms

    Text Solution

    |

  14. The sum of an infinite series is 15 and the sum of the squares of thes...

    Text Solution

    |

  15. Insert three geometric means between 1 and 256.

    Text Solution

    |

  16. In the sum to infinity of the series 3+(3+x) (1)/(4) + (3+2x)(1)/(4^(2...

    Text Solution

    |

  17. Find the sum to n terms of the series 3.8 +6.11 +9.14 + ...

    Text Solution

    |

  18. Find the sum 5^(2)+ 6^(2) + 7^(2) + ... + 20^(2).

    Text Solution

    |

  19. If in a geometric progression consisting of positive terms, each term ...

    Text Solution

    |

  20. If the first term of an infinite G.P. is 1 and each term is twice the ...

    Text Solution

    |

  21. If fifth term of a G.P. is 2, then the product of its first 9 terms is

    Text Solution

    |