Home
Class 11
MATHS
The first term of a G.P. is 2 and each o...

The first term of a G.P. is 2 and each of its term is equal to sum of the succeding terms of the G.P. Find the G.P.

Text Solution

Verified by Experts

The correct Answer is:
N/a

`"Let the G.P. be "a+ar+ar^(2)+ar^(3)+...oo" Here "a=2 and a=ar+ar^(2)+ar^(3)+...oo`
`rArr" "a=(ar)/(1-r)`
`rArr" "1=(r)/(1-r)`
`rArr" "1-r=r`
`rArr" "r=(1)/(2)`
`thereforeG.P. = 2+1+(1)/(2)+(1)/(4)+...oo.`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Exercise 9A|4 Videos
  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN|Exercise Exercise 9B|17 Videos
  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|12 Videos
  • SETS

    NAGEEN PRAKASHAN|Exercise MISC Exercise|16 Videos

Similar Questions

Explore conceptually related problems

The first term of an infinite G..P is 1 and any term is equal to the sum of all the succeeding terms. Find the series.

The sum of first two terms of an infinite G.P.is 5 and each term is three xx the sum of the succeeding terms.Find the G.P.

The first term of an infinite G.P. is 1 and every term is equals to the sum of the successive terms, then its fourth term will be

The first term of an infinite G.P.is 1 and every term is equals to the sum of the successive term,then its fourth term will be

The fifth term of a G.P. is 32 and common ratio is 2 , then the sum of first 14 terms of the G.P. is

In an infinite G.P.,each term is equal to the sum of all the succeeding terms.The common ratio of the G.Pis

The sum of the fist ten terms of an A.P. , equals 155 and the sum of the first two terms of a G.P. equals 9. The first term of the A.P. is equal to the common ratio of the G.P. and the common difference of the A.P. is equal to the first term G.P.. Give that the common difference of the A.P. is less then unity, which of the following is correct ?

If the first term of G.P. is 7, its n^(th) term is 448 and sum of first n terms is 889, then find the fifth term of G.P.

NAGEEN PRAKASHAN-SEQUENCE AND SERIES-Miscellaneous Exercise
  1. The first term of a G.P. is 2 and each of its term is equal to sum of ...

    Text Solution

    |

  2. 32. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A.P. is...

    Text Solution

    |

  3. If the sum of three numbers in A.P., is 24 and their product is 440...

    Text Solution

    |

  4. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

    Text Solution

    |

  5. Find the sum of all numbers between 200 and 400 which are divisible...

    Text Solution

    |

  6. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

    Text Solution

    |

  7. Find the sum of all two digit numbers which when divided by 4, yiel...

    Text Solution

    |

  8. If f is a function satisfying f(x + y) = f(x) f(y) for all x, y in N s...

    Text Solution

    |

  9. The sum of some terms of G. P. is 315 whose first term and the commo...

    Text Solution

    |

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

    Text Solution

    |

  11. The sum of three numbers m GP is 56. If we subtract 1.7,21 from the...

    Text Solution

    |

  12. A. G.P. consists of an even number of terms. If the sum of all the ter...

    Text Solution

    |

  13. The sum of the first four terms of an A.P. is 56. The sum of the last ...

    Text Solution

    |

  14. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0) , then show tha...

    Text Solution

    |

  15. if S is the sum , P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  16. If pth,qth and rth terms of an A.P. are a, b, c respectively, then sho...

    Text Solution

    |

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

    Text Solution

    |

  18. If a ,b ,c are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in...

    Text Solution

    |

  19. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

    Text Solution

    |

  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m ...

    Text Solution

    |

  21. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,1/d ,1/eare in A....

    Text Solution

    |