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__________.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    VMC MODULES ENGLISH|Exercise LEVEL-2|34 Videos

  • REVISION TEST-2 JEE

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos

Similar Questions

Explore conceptually related problems

Let a_1,a_2,a_3,... be in harmonic progression with a_1=5a n da_(20)=25. The least positive integer n for which a_n<0 a. 22 b. 23 c. 24 d. 25

Let a_1, a_2, a_3, ,a_(101) are in G.P. with a_(101)=25a n dsum_(i=1)^(201)a_1=625. Then the value of sum_(i=1)^(201)1/(a_1) equals____________.

If a_1,a_2,……….,a_n are in H.P. then expression a1a2+a2a3+......+a_n-1an

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 a_1,a_2,a_3….., a_(101) are in G.P with a_(101) =25 and Sigma_(i=1)^(201) a_i=625 Then the value of Sigma_(i=1)^(201) 1/a_i eaquals _______.

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_1,a_2,a_3,...,a_(n+1) are in A.P. , then 1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1)) is

Let A_1 , A_2 …..,A_3 be n arithmetic means between a and b. Then the common difference of the AP is

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then common ratio of G.P can be

The terms a_1, a_2, a_3 from an arithmetic sequence whose sum s 18. The terms a_1+1,a_2, a_3,+2, in that order, form a geometric sequence. Then the absolute value of the sum of all possible common difference of the A.P. is ________.

VMC MODULES ENGLISH-SEQUENCE AND SERIES -JEE MAIN & Advance ( ARCHIVE)
  1. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  2. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

    Text Solution

    |

  3. Let S(1),S(2),"…." be squares such that for each n ge 1, the length o...

    Text Solution

    |

  4. Let a1,a2,a3,... be in harmonic progression with a1=5a n da(20)=25. Th...

    Text Solution

    |

  5. Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...

    Text Solution

    |

  6. If m is the A.M of two distict real numbers l and n (l, n gt 1)and G1,...

    Text Solution

    |

  7. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

    Text Solution

    |

  8. If alpha in (0,pi/2),t h e nsqrt(x^2+x)+(tan^2alpha)/(sqrt(x^2+x)) is ...

    Text Solution

    |

  9. If a1,a2,a3,....an are positive real numbers whose product is a fixed ...

    Text Solution

    |

  10. If a ,b ,c ,d are positive real umbers such that a=b+c+d=2,t h e nM=(a...

    Text Solution

    |

  11. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Let (a1,a2,a3….,a11) be real numbers satsfying a1=15,27-2a2 gt 0 and ...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  17. Let x be the arithmetic mean and y ,z be tow geometric means between a...

    Text Solution

    |

  18. Let the harmonic mean and geometric mean of two positive numbers be in...

    Text Solution

    |

  19. The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1,a^8 ...

    Text Solution

    |

  20. Let pa n dq be the roots of the equation x^2-2x+A=0 and let ra n ds be...

    Text Solution

    |