Home
Class 12
MATHS
Let a(1),a(2),a(3),….,a(4001) is an A.P....

Let `a_(1),a_(2),a_(3),….,a_(4001)` is an `A.P.` such that `(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+...+(1)/(a_(4000)a_(4001))=10`
`a_(2)+a_(4000)=50`.
Then `|a_(1)-a_(4001)|` is equal to

A

`20`

B

`30`

C

`40`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(a_(2)-a_(1))/(a_(1)a_(2))+(a_(3)-a_(2))/(a_(2)a_(3))+...+(a_(4001)-a_(4000))/(a_(4001)a_(4000))=10d`
`:.(1)/(a_(1))-(1)/(a_(4001))=10d`
`:. (4000d)/(a_(1)a_(4001))=10d`
`:.a_(1)a_(4001)=400`
also `a_(1)+a_(4001)=50` ,brgt `implies |a_(1)-a_(4001)|^(2)=2500-1600`
`implies|a_(1)-a_(4001)|=30`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) -a_(2))^(2) = (a_(1)-a_(4))^(2)

If a_(1),a_(2),a_(3),………. are in A.P. such that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225, then a_(1) + a_(2) + a_(3) + …… a_(23) + a_(24) =

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If a_(1), a_(2), . . . , a_(n) is a sequence of non-zero number which are in A.P., show that (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+. . . + (1)/(a_(n)a_(1))= (2)/(a_(1) + a_(n)) [(1)/(a_(1))+(1)/(a_(2))+. . . +(1)/(a_(n))]

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

Let A_(1), A_(2), A_(3),…,A_(n) be the vertices of an n-sided regular polygon such that (1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n.

Let a_(1),a_(2),a_(3),a_(4)anda_(5) be such that a_(1),a_(2)anda_(3) are in A.P., a_(2),a_(3)anda_(4) are in G.P., and a_(3),a_(4)anda_(5) are in H.P. Then, a_(1),a_(3)anda_(5) are in

CENGAGE ENGLISH-PROGRESSION AND SERIES-Single correct Answer
  1. If a1,a2,a3,... are in A.P. and ai>0 for each i, then sum(i=1)^n n/(a(...

    Text Solution

    |

  2. Between the numbers 2 and 20, 8 means are inserted. Then their sum is

    Text Solution

    |

  3. Let a(1),a(2),a(3),….,a(4001) is an A.P. such that (1)/(a(1)a(2))+(1)/...

    Text Solution

    |

  4. An A.P. consist of even number of terms 2n having middle terms equal t...

    Text Solution

    |

  5. If the sum of the first 100 terms of an AP is -1 and the sum of even t...

    Text Solution

    |

  6. Given the sequence of numbers x(1),x(2),x(3),x(4),….,x(2005), (x(1))/(...

    Text Solution

    |

  7. If b-c, bx-cy, bx^(2)-cy^(2) (b,c ne 0) are in G.P, then the value of ...

    Text Solution

    |

  8. If a(1),a(2),a(3),… are in G.P., where a(i) in C (where C satands for ...

    Text Solution

    |

  9. If a, b, c are real numbers forming an A.P. and 3+a, 2+b, 3+c are in G...

    Text Solution

    |

  10. a, b, c, d are in increasing G.P. If the AM between a and b is 6 and t...

    Text Solution

    |

  11. The numbers a,b,c are in A.P. and a+b+c=60. The numbers (a-2), b, (c+3...

    Text Solution

    |

  12. a, b, c are positive integers formaing an incresing G.P. and b-a is a ...

    Text Solution

    |

  13. The first three terms of a geometric sequence are x, y,z and these hav...

    Text Solution

    |

  14. If an infinite G.P. has 2nd term x and its sum is 4, then prove that x...

    Text Solution

    |

  15. In a GP, the ratio of the sum of the first eleven terms of the sum of ...

    Text Solution

    |

  16. The number of ordered pairs (x,y) , where x, y in N for which 4, x, y ...

    Text Solution

    |

  17. If a+c, a+b, b+c are in G.P and a,c,b are in H.P. where a,b,c gt 0, th...

    Text Solution

    |

  18. If a,b,c are in H.P, b,c,d are in G.P and c,d,e are in A.P. , then the...

    Text Solution

    |

  19. If x gt 1, y gt 1, z gt 1 are in G.P., then log(ex)e, log(ey)e , log(e...

    Text Solution

    |

  20. If x,y,z are in G.P. (x,y,z gt 1) , then (1)/(2x+log(e)x), (1)/(4x+log...

    Text Solution

    |