Home
Class 14
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__________.

A

10

B

9

C

5

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • RATIO, PROPORTION & VARIATION

    QUANTUM CAT|Exercise QUESTION BANK|238 Videos

  • SET THEORY

    QUANTUM CAT|Exercise QUESTION BANK|81 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.

a_1, a_2, a_3 …..a_9 are in GP where a_1 lt 0, a_1 + a_2 = 4, a_3 + a_4 = 16 , if sum_(i=1)^9 a_i = 4 lambda then lambda is equal to

QUANTUM CAT-SEQUENCE, SERIES & PROGRESSIONS-QUESTION BANK
  1. The arithmetic mean and geometric mean of two numbers are 10 and 18 re...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Let a1,a2 ,…. , a10 be in A.P. and h1,h2 …. h10 be in H.P. If a1=h1...

    Text Solution

    |

  6. For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) ...

    Text Solution

    |

  7. What is the sum of the series 1+(1)/(2)+(1)/(4)+(1)/(8)+. . .?

    Text Solution

    |

  8. If apq=9b and a, b, p, q are positive real numbers, find the minimum v...

    Text Solution

    |

  9. kamal goes to a place at a speed of 10 km/hr and return home at speed ...

    Text Solution

    |

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

    Text Solution

    |

  11. If a,b,c are positive real numbers then (1+a)^7(1+b)^7)1+c)^7 (A) lt7^...

    Text Solution

    |

  12. The least positive integer n for which ((1+i sqrt3)/(1-isqrt3))^(n)=1,...

    Text Solution

    |

  13. A bacteria gives birth to two new bacterias in each second and the lif...

    Text Solution

    |

  14. Find the sum of 6 terms of the series 2+6+18+…..

    Text Solution

    |

  15. If Um be defined as the sum of m terms of the series V, where V=Sm+S(m...

    Text Solution

    |

  16. Let a1 , a2 ,a3, …., an be an A.P. and S1 , S2 and S3 be the sum of fi...

    Text Solution

    |

  17. Consider the sets T(n)={n, n+3, n+5, n+7, n+9} where n=1,2,3,.....,9...

    Text Solution

    |

  18. If {x} is the least integer greater than or equal to x, then find the ...

    Text Solution

    |

  19. If [x] is the greatest integer less than or equal to x, then find the ...

    Text Solution

    |

  20. Shaan got a total of Rs. 912 in the denomination of equal numbers of R...

    Text Solution

    |