Home
Class 12
MATHS
Let a1, a2, a3, ,a(100) be an arithmeti...

Let `a_1, a_2, a_3, ,a_(100)` be an arithmetic progression with `a_1=3a n ds_p=sum_(i=1)^p a_i ,1lt=plt=100.` For any integer `n` with `1lt=nlt=20 ,` let`m=5ndot` If `(S_m)/(S_n)` does not depend on `n ,` then `a_2` is__________.

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -I Previous Year /JEE Main|19 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

Let a_(1),a_(2),a_(3),...,a_(100) be an arithmetic progression with a_(1)=3 and s_(p)=sum_(i=1)^(p)a_(i),1<=p<=100. For any integer n with 1<=n<=20, let m=5n If (S_(m))/(S_(n)) does not depend on n, then a_(2)

If a_1,a_2,a_3 …. are in harmonic progression with a_1=5 and a_20=25 . Then , the least positive integer n for which a_n lt 0 , is :

let a_1,a_2,a_3........be an arithmetic progression with comman difference 2. let S_n be the sum of first n terms of the sequence . if S_(3n)/s_n does not depend on n then the sim of the first 10 terms.

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

Let a_1,a_2,a_3,.... are in GP. If a_n>a_m when n>m and a_1+a_n=66 while a_2*a_(n-1)=128 and sum_(i=1)^n a_i=126 , find the value of n .

If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

Let (1+x^2^2)^2(1+x)^n = sum _(k=0)^(n+4)a_k x^k. If a_1,a_2,a_3 are in rithmetic progression find n.

MOTION-SEQUENCE & SERIES -Exercise -4 Level -II Previous Year /JEE Advanced
  1. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  2. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  3. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  4. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  5. A straight line through the vertex P of a triangle PQR intersects the ...

    Text Solution

    |

  6. Suppose four distinct positive numbers a1,a2,a3,a4 are in G.P. Let b1=...

    Text Solution

    |

  7. In the sum of first n terms of an A.P. is cn^2, then the sum of square...

    Text Solution

    |

  8. Let Sk ,k=1,2, ,100 , denotes thesum of the infinite geometric series ...

    Text Solution

    |

  9. Let a(1),a(2),a(3),"........."a(11) be real numbers satisfying a(1)=15...

    Text Solution

    |

  10. The minimum value of the sum of real number a^(-5),a^(-4),3a^(-3),1,a^...

    Text Solution

    |

  11. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

  12. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

    Text Solution

    |

  13. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  14. Let an denote the number of all n-digit positive integers formed by th...

    Text Solution

    |

  15. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/2)k^(2). Then S(n) can take value...

    Text Solution

    |

  16. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  17. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

    Text Solution

    |

  18. Suppose that all the terms of an arithmetic progression (A.P.) are nat...

    Text Solution

    |

  19. Let bi gt 1 for i = 1, 2, ...., 101. Suppose loge b1, loge b2, ...., l...

    Text Solution

    |

  20. Let X be the set consisting of the first 2018 terms of the arithmet...

    Text Solution

    |