Home
Class 12
MATHS
Let an be the nth term of a G.P. of posi...

Let `a_n` be the nth term of a G.P. of positive numbers. Let `sum_(n=1)^(100)a_(2n)=alphaa n dsum_(n=1)^(100)a_(2n-1)=beta` , such that `alpha!=beta` , then the common ratio is `alpha//beta` b. `beta//alpha` c. `sqrt(alpha//beta)` d. `sqrt(beta//alpha)`

A

`(alpha )/(beta)`

B

`(beta)/(alpha)`

C

`sqrt((alpha)/(beta))`

D

`sqrt((beta)/(alpha))`

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - C) More than one option are correct|11 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - D) Linked Comprehension|11 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - A) One option is correct|60 Videos
  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos
  • SETS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION-I(Aakash Challengers Questions)|4 Videos

Similar Questions

Explore conceptually related problems

Let a_n be the nth term of a G.P. of positive numbers. Let sum_(n=1)^(100)a_(2n)=alpha and sum_(n=1)^(100)a_(2n-1)=beta , such that alpha!=beta , then the common ratio is (a) alpha//beta b. beta//alpha c. sqrt(alpha//beta) d. sqrt(beta//alpha)

Let a_n be the nth therm of a G.P of positive numbers .Let Sigma_(n=1)^(100) a_(2n)=alpha and Sigma_(n=1)^(100)a_(an-1)=beta then the common ratio is

Let a_(n) be the nth term of an AP, if sum_(r=1)^(100)a_(2r)= alpha " and "sum_(r=1)^(100)a_(2r-1)=beta , then the common difference of the AP is

Let a_n be the n^(t h) term of an A.P. If sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta, then the common difference of the A.P. is (a) alpha-beta (b) beta-alpha (c) (alpha-beta)/2 (d) None of these

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)=beta, then the value of (log)_(10)4100 in terms of alpha and beta is equal to a. alpha+9beta b. alpha+12beta c. 12alpha+beta d. 9alpha+beta

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are (alpha+1//beta)a n d(beta+1//alpha) .

If alpha,beta are the roots of the equation ax^(2)-bx+b=0 , prove that sqrt((alpha)/(beta))+sqrt((beta)/(alpha))-sqrt((b)/(a))=0 .

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta

If alpha, beta be the roots of px^(2)-qx +q=0 , then show that sqrt((alpha)/(beta)) +sqrt((beta)/(alpha)) - sqrt((g)/(p))=0 .

The value of the integral int_alpha^beta (1)/(sqrt((x-alpha)(beta-x)))dx " for "beta gt alpha , is

AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Assignment (SECTION - B) One option is correct
  1. The sum of the first 100 terms common to the series 17, 21, 25, 29...

    Text Solution

    |

  2. If the sixth term of a GP be 2, then the product of first eleven te...

    Text Solution

    |

  3. Let an be the nth term of a G.P. of positive numbers. Let sum(n=1)^(10...

    Text Solution

    |

  4. The series . (2x)/(x + 3) + ((2x)/(x + 3))^(2) + ((2x)/(x + 3))^(3) +...

    Text Solution

    |

  5. Four geometric mens are inserted between the number 2^(11) - 1 an...

    Text Solution

    |

  6. Find the values of x in (-pi,pi) which satisfy the equation 8^(1+|cosx...

    Text Solution

    |

  7. If one G.M., G and two A.M's p and q be inserted between two given num...

    Text Solution

    |

  8. about to only mathematics

    Text Solution

    |

  9. Let a, b be the roots of the equation x^(2) - 4 x +k(1) = 0 and c ...

    Text Solution

    |

  10. If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...

    Text Solution

    |

  11. Sum of the series 1+2.2+3.2^2 +4.2^3+.....+100.2^99 is

    Text Solution

    |

  12. If 3+1/4(3+p)+1/(4^2)(3+2p)+... + oo=8, then p

    Text Solution

    |

  13. The value of 2^(1/4).4^(1/8).8^(1/16),,,,,,,oo is equal to.

    Text Solution

    |

  14. Let S denotes the infinite sum 2 + 5x + 9x^(2) + 14x^(3) + 2x^(4) ...

    Text Solution

    |

  15. The value of x + y + z is 15 if a, x, y, z, b are in A.P. while t...

    Text Solution

    |

  16. If x , y, z are positive reals satisfying 4xy + 6yz + 8 zx = 9 , ...

    Text Solution

    |

  17. The sum to 100 terms of the series 1.2.3. + 2.3.4. + 3.4.5. + …+ n...

    Text Solution

    |

  18. The sum of the first n terms of the series 1^2+2xx2^2+3^2+2xx 4^2+5^2+...

    Text Solution

    |

  19. If x,y, z and w are non-zero real numbers and x^(2) + 5y^(2) + 5z^...

    Text Solution

    |

  20. If x^(18)=y^(21)=z^(28), then 3,3 log(y)x,3log(z)y,7log(x)z are in

    Text Solution

    |