Home
Class 11
MATHS
A. G.P. consists of an even number of te...

A. G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.

Text Solution

Verified by Experts

Let there be 2n terms in the G.P. with first term a and common ratio r.
Then,
Sum of all the terms = 5 (Sum of the terms occupying the odd places)
⇒`a_1​+a_2​+...+a_(2n)​=5(a_1​+a_3​+a_5​+...+a_(2n−1)​)`
...
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|157 Videos
  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|5 Videos

Similar Questions

Explore conceptually related problems

A G.P.consists of an even number of terms.If the sum of all the terms is 5 xx the sum of terms occupying odd places,then find its common ratio.

If each term of an infinite G.P.is twice the sum of the terms following it,then find the common ratio of the G.P.

A G.P consists of 2n terms . If the sum of the terms . If the sum of the terms occupying the odd place is S_(1), and that of the terms in the even places is S_(2) then find the common ratio of the progression

The first terms of a G.P.is 1. The sum of the third and fifth terms is 90. Find the common ratio of the G.P.

A geometric progression consists of 500 terms. Sum of the terms occupying the odd places is P_1 and the sum of the terms occupying the even places is P_2 . Find the common ratio.

If the sum of first 10 terms is 33 times the sum of first 5 terms of G.P. find the common ratio.

RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. How many terms of the G.P. 3,3//2,3//4, be taken together to make (30...

    Text Solution

    |

  2. A person has 2 parents, 4 grandparents, 8 great grand parents, and so ...

    Text Solution

    |

  3. A. G.P. consists of an even number of terms. If the sum of all the t...

    Text Solution

    |

  4. Find the sum to infinity of GP -5/4, 5/16,-5/64......

    Text Solution

    |

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

    Text Solution

    |

  6. If b=a+a^2+a^3+ dotoo prove that a=b/(1+bdot)

    Text Solution

    |

  7. The first term of G.P. is 2 and the sum to infinity is 6. Find the com...

    Text Solution

    |

  8. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

    Text Solution

    |

  9. Use geometric series to express 0. 555... =0. overline5 as\ a rationa...

    Text Solution

    |

  10. The inventor of the chess board suggested a reward of one grain of whe...

    Text Solution

    |

  11. The sum of an infinite geometric series is 15 and the sum of the squ...

    Text Solution

    |

  12. Find the sum of the following series to infinity: 1-1/3+1/(3^2)-1/(3^3...

    Text Solution

    |

  13. Find the sum of the following series to infinity: 2//5+3//5^2\ +2//5^3...

    Text Solution

    |

  14. Find the sum of the following series to infinity: 1/3+1/(5^2)+1/(3^3)+...

    Text Solution

    |

  15. Find the sum of the following series to infinity: 8+4sqrt(2)+4+oo

    Text Solution

    |

  16. Find the sum of the following series to infinity: 10-9+8. 1-7. 29+oo

    Text Solution

    |

  17. Find the value of 9^(1/3). 9^(1/9). 9^(1/27)...up to oo.

    Text Solution

    |

  18. Prove that: 2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2.

    Text Solution

    |

  19. The terms of an infinitely decreasing G.P. in which all the terms are ...

    Text Solution

    |

  20. Express the recurring decimal 0.125125125 ... as a rational number.

    Text Solution

    |