Home
Class 12
MATHS
Let an is a positive term of a GP and su...

Let `a_n` is a positive term of a GP and `sum_(n=1)^100 a_(2n + 1)= 200, sum_(n=1)^100 a_(2n) = 200`, find `sum_(n=1)^200 a_(2n) =?

Text Solution

Verified by Experts

The correct Answer is:
150
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES CONCEPT-BASED (Single Correct Answer Type Questions)|15 Videos

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES LEVEL-1 (Single Correct Answer Type Questions)|65 Videos

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES LEVEL -2 (SINGLE CORRECT ANSWER TYPE QUESTIONS)|12 Videos

  • PROBABILITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Papers|21 Videos

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from previous Years. B - architecture entrance examination papers|16 Videos

Similar Questions

Explore conceptually related problems

If a_(n)=(n)/((n+1)!) then find sum_(n=1)^(50)a_(n)

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 alpha/ beta b.beta/ alpha c.sqrt(alpha/ beta) d.sqrt(beta/ alpha)

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

If a_(n)=n(n!), then sum_(r=1)^(100)a_(r) is equal to

Let a_(n) be the n^(th) 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 alpha-beta(b)beta-alpha(alpha-beta)/(2)quad (d) None of these

For a sequence, if a_(1)=2 and (a_(n+1))/(a_(n))=(1)/(3). Then, sum_(r=1)^(20) a_(r) is

If i^(2)=-1 then the value of sum_(n=1)^(200)i^(n) is

For any n positive numbers a_(1),a_(2),…,a_(n) such that sum_(i=1)^(n) a_(i)=alpha , the least value of sum_(i=1)^(n) a_(i)^(-1) , is

MCGROW HILL PUBLICATION-PROGRESSIONS-SOLVED EXAMPLES LEVEL (Numerical Answer Type Questions)
  1. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

    Text Solution

    |

  2. If x gt 0 and log(3) (x)+log(3)(x^(1//3))+log(3)(x^(1//9))+log(3)(x^(1...

    Text Solution

    |

  3. If a1,a2,a3,a4 are in HP , then 1/(a1a4)sum(r=1)^3ar a(r+1) is roo...

    Text Solution

    |

  4. Let s(n)=1+(1)/(3)+(1)/(3^(2))+…+(1)/(3^(n-1)). The least value of n i...

    Text Solution

    |

  5. Let a(n) be the nth term of a G.P. of positive real numbers. If overse...

    Text Solution

    |

  6. Let [x] = greatest integer le x. Suppose roots of the quadratic equati...

    Text Solution

    |

  7. three number a,b,c are in GP such that : (i) a+b+c=70 (ii) 4a,5b,4c a...

    Text Solution

    |

  8. Suppose a(1),a(2),…a(n) are positive real numbers which are in A.P. If...

    Text Solution

    |

  9. Suppose alpha, gamma are roots of the equation ax^(2)-4x+1=0 and beta,...

    Text Solution

    |

  10. Let an is a positive term of a GP and sum(n=1)^100 a(2n + 1)= 200, sum...

    Text Solution

    |

  11. Suppose a(1),a(2),… are real numbers such that sqrt(a(1))+sqrt(a(2)-1)...

    Text Solution

    |

  12. Let S=overset(oo)underset(n=1)Sigma(5^(n)7^(n))/((7^(n)-5^(n))(7^(n+1)...

    Text Solution

    |

  13. Let S=overset(oo)underset(k=1)Sigma (k(10)^(k)+2^(k+1)5^(k))/(5^(k)2^(...

    Text Solution

    |

  14. Consider an A.P. a1, a2, an , and the G.P. b1,b2, ,bn , such that a...

    Text Solution

    |

  15. Suppose a(1),a(2),…a(201) gt 0 and are in G.P. If a(101)=36 and overse...

    Text Solution

    |

  16. Let P(n) denote the product of first n terms of the G.P. 16, 4, 1, 1/4...

    Text Solution

    |

  17. Suppose x, y in N and log(5)(x)+log(5)(x^(1//2))+log(5)(x^(1//4))+….=y...

    Text Solution

    |

  18. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

    Text Solution

    |

  19. Suppose 1 lt a lt sqrt(e) and log(e)a^(2)+(log(e)a^(2))^(2)+(log(e)a^(...

    Text Solution

    |

  20. For k=2,3,…, let S(k) denote the sum of the infinite G.P. whose first ...

    Text Solution

    |