Home
Class 11
MATHS
Let a(n) be the nth term of an AP, if su...

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

A

`15`

B

`9`

C

`45`

D

`35`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SETS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (FILLERS)|10 Videos

  • SETS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (TRUE/FALSE)|6 Videos

  • SETS

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)|17 Videos

  • SEQUENCE AND SERIES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems -Question of Module|19 Videos

  • STATISTICS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE (KNOWLEDGE TEST)|9 Videos

Similar Questions

Explore conceptually related problems

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 -

sum_(r=1)^n(2r+1)=...... .

Knowledge Check

  • If the sum of n terms of an AP is given by S_(n) = 3n+ 2n^(2) , then the common difference of the AP is

    A
    3
    B
    2
    C
    6
    D
    4

    • Similar Questions

    Explore conceptually related problems

    A person is to count 4500 currency notes. Let a_(n) denotes the number of notes he counts in the nth minute. If a_(1)=a_(2)="........"=a_(10)=150" and "a_(10),a_(11),"......", are in AP with common difference -2 , then the time taken by him to count all notes is

    If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

    If sum_(r=1)^(n)T_(r)=(n)/(8)(n+1)(n+2)(n+3)," find "sum_(r=1)^(n)(1)/(T_(r)) .

    Let z_(r),r=1,2,3,...,50 be the roots of the equation sum_(r=0)^(50)(z)^(r)=0 . If sum_(r=1)^(50)1/(z_(r)-1)=-5lambda , then lambda equals to

    Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

    Let |Z_(r) - r| le r, Aar = 1,2,3….,n . Then |sum_(r=1)^(n)z_(r)| is less than

    If the sum of n terms of an A.P. is nP+1/2n(n-1)Q , where P and Q are constants, find the common difference.

    Home
    Profile