Home
Class 11
MATHS
Consider an A.P. with first term 'a'. Le...

Consider an A.P. with first term 'a'. Let `S_(n)` denote the sum its terms. If `(S_(kx))/(S_(x))` is independent of x, then `S_(n)=`

A

`n^(2)a`

B

na

C

`2n^(2)a`

D

`(n^(2)+n)a`

Text Solution

Verified by Experts

The correct Answer is:
A
Let d be common difference. Then, d=2a (See Illustration 8).
`:." "S_(n)=(n)/(2){2a+(n-1)d}=(n)/(2){2a+(n-1)xx2a}=n^(2)a`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|80 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|13 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Consider an A.P.with first term a and common difference d.Let S_(k) denote the sum of the first k terms.If (S_(kx))/(S_(x)) is independent of x, then

If S_n denote the sum of n terms of an A.P. with first term a and common difference d such that (S_x)/(S_(k x)) is independent of x , then d=a (b) d=2a (c) a=2d (d) d=-a

Let S_(n) denote the sum of first n terms of an A.P.If S_(2n)=3S_(n), then find the ratio S_(3n)/S_(n)

If S_(n) denote the sum of first n terms of an A.P. whose first term is a and S_(nx)/S_(x) is independent of x, then S_(p)=p^(3) b.p^(2)a .pa^(2) d.a^(3)

Let S_(n) denote the sum of the first n terms of an AP. If S_(4) = 16 and S_(6) = -48 , then S_(10) is equal to

Let S_(n) denote the sum of the first n terms of an A.P.. If S_(4)=16 and S_(6)=-48, then S_(10) is equal to :

Consider the A.P. 50,48,46,44 ……. If S _(n) denotes the sum to n terms of this A.R. then

For an A.P. if the first term is 8 and the common difference is 8, then S_(n) =

OBJECTIVE RD SHARMA-SEQUENCES AND SERIES-Chapter Test
  1. Consider an A.P. with first term 'a'. Let S(n) denote the sum its term...

    Text Solution

    |

  2. Let H(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n), then the sum to n terms...

    Text Solution

    |

  3. The sum to n terms of the series 1/2+3/4+7/8+15/16+..... is given by

    Text Solution

    |

  4. If A(1),A(2) are between two numbers, then (A(1)+A(2))/(H(1)+H(2)) is ...

    Text Solution

    |

  5. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

    Text Solution

    |

  6. Given that n arithmetic means are inserted between two sets of numbers...

    Text Solution

    |

  7. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  8. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  9. If in an AP, t1 = log10 a, t(n+1) = log10 b and t(2n+1) = log10 c then...

    Text Solution

    |

  10. Find the sum of the series: 1^2-2^2+3^2-4^2+.....-2008^2+2009^2.

    Text Solution

    |

  11. If4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)," where "a,b,c are non-zero num...

    Text Solution

    |

  12. If Sn denotes the sum of n terms of an A.P. whose common difference is...

    Text Solution

    |

  13. The sides of a right angled triangle arein A.P., then they are in the...

    Text Solution

    |

  14. Find the sum of all the 11 terms of an AP whose middle most term is 30...

    Text Solution

    |

  15. The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...

    Text Solution

    |

  16. If three numbers are in G.P., then the numbers obtained by adding the ...

    Text Solution

    |

  17. If p,q,r,s in N and the are four consecutive terms of an A.P., then p^...

    Text Solution

    |

  18. If x,y,z be three positive prime numbers. The progression in which sqr...

    Text Solution

    |

  19. If 1/(b-a)+1/(b-c)=1/a+1/c , then a ,b ,a n dc are in H.P. a ,b ,a n d...

    Text Solution

    |

  20. If three numbers are in H.P., then the numbers obtained by subtracting...

    Text Solution

    |

  21. The first three of four given numbers are in G.P. and their last three...

    Text Solution

    |