Home
Class 12
MATHS
Let A be the sum of the first 20 terms a...

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series `1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+...` If `B-2A=100lambda` then `lambda` is equal to (1) 232 (2) 248 (3) 464 (4)496

A

248

B

464

C

496

D

232

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise (JA)|12 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise S-2|12 Videos

  • RACE

    ALLEN|Exercise Race 21|10 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|8 Videos

Similar Questions

Explore conceptually related problems

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^(2)+2.2^(2)+3^(2)+2.4^(2)+5^(2)+2.6^(2)+... If B-2A=100 lambda then lambda is equal to (1)232(2)248 (3) 464 (4) 496

The sum of the first n terms of the series 1^(2)+2.2^(2)+3^(2)+2.4^(2)+5^(2)+2.6^(2)+... is

Find the sum of first n terms and the sum of first 5 terms of the geometric series 1+(2)/(3)+

The sum first 19 terms of the series 1^2+2(2^2)+3^2+2(4^2)+5^2+... is :

The sum of the first five terms of the series 3 +4 1/2+6 3/4+...=

Find the sum of n terms of the series 1.2^(2)+2.3^(2)+3.4^(2)+

Sum to 20 terms of the series 1.3^(2)+2.5^(2)+3.7^(2)+... is

Find the sum to n terms of the series 1*2^(2)+2*3^(2)+3*4^(2)+...

ALLEN-SEQUENCE AND PROGRESSION-Exercise (JM)
  1. If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P...

    Text Solution

    |

  2. If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3...

    Text Solution

    |

  3. If, for a positive integer n , the quadratic equation, x(x+1)+(x-1)(x+...

    Text Solution

    |

  4. For any three positive real numbers a, b and c, 9(25a^2+b^2)+25(c^2-3a...

    Text Solution

    |

  5. Let a, b, c in R. If f (x) = ax^(2) + bx + c is such that a + b + c = ...

    Text Solution

    |

  6. Let a(1), a(2), a(3).... A(49) be in A.P. such that sum(k =0)^(12) a(4...

    Text Solution

    |

  7. Let A be the sum of the first 20 terms and B be the sum of the first 4...

    Text Solution

    |

  8. If a, b and c be three distinct real number in G.P. and a + b + c = xb...

    Text Solution

    |

  9. Let a(1), a(2) ......, a(30) be an A.P., S = sum(i=1)^(30) a(i) and T...

    Text Solution

    |

  10. Find sun of first 15 term of series 1+6+(9(1^2+2^2+3^2))/(7)+(12(1^2+...

    Text Solution

    |

  11. If x and y are positive real numbers and m, n are any positive integ...

    Text Solution

    |

  12. If sin^4 alpha + 4 cos^4 beta + 2 = 4sqrt2 sin alpha cos beta ; alpha,...

    Text Solution

    |

  13. The sum of all natural number 'n' such that 100 lt n lt 200 and H.C.F....

    Text Solution

    |

  14. If a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^...

    Text Solution

    |

  15. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

    Text Solution

    |

  16. The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) ...

    Text Solution

    |

  17. Let numbers a(1),a(2)…a(16) are in AP and a(1)+a(4)+a(7)+a(10)+a(13)+a...

    Text Solution

    |

  18. Let a,b and c be in G.P. with common ratio r, where a != 0 and 0 lt r ...

    Text Solution

    |

  19. If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = ...

    Text Solution

    |

  20. If alpha, beta and gamma are three consecutive terms of a non-constant...

    Text Solution

    |