Home
Class 12
MATHS
There are m A.P. Whose common differenc...

There are m A.P. Whose common differences are 1,2,3,.. M respectively, the first term of each being unity. Show that the sum of their nth terms is `(m)/(2)(mn -m+n+1)`.

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)|124 Videos
  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos
  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise TRIGONOMETRY|148 Videos
  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos
  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

The nth term of an A.P. is p, show that, the sum of its first (2n-1) terms is (2n-1)p.

If the nth term of a G.P. be p, then show that the product of its first (2n-1) terms is p^(2n-1) .

The mth term of a H.P is n and the nth term is m . Proves that its rth term is (mn)/r

Find the 12th term of a series in A.P., whose sum of n terms is 4n^(2) + 3n .

The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

The rth terms of an A.P is n and it's nth term is r, show that its mth term is r+n - m.

If the first term of an A.P. is 2 and common difference is 4, then the sum of its first 40 terms is-

if the Pth term of an A.P. is q and qth term is P.Then show that the nth term is p+q-n

If the sum of first n terms of a G.P is p and the sum of the first 2n terms is 3p,show that the sum of first 3n terms is7p.

The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2) . Show that the ratio mth and nth term is (2m-1) : (2n-1).

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the amplitude of z=1+i "tan" (3pi)/(5)

    Text Solution

    |

  2. Find the modulus and amplitude of z="sin" (6pi)/(5)+I (1+"cos" (6pi)...

    Text Solution

    |

  3. There are m A.P. Whose common differences are 1,2,3,.. M respectively...

    Text Solution

    |

  4. If S(1),S(2),S(3),...S(m) be the sum of first n terms of n A.P. Whose...

    Text Solution

    |

  5. Show that the sum of the numbers in the n th bracket of the series (1)...

    Text Solution

    |

  6. Show that the following two A.P. is have 14 common terms 3,7,11,15...,...

    Text Solution

    |

  7. Show that there are 17 identical terms in the following two A.P. 2,5,8...

    Text Solution

    |

  8. Find the n th term and the sum of first n terms of thefollowing sequen...

    Text Solution

    |

  9. Solve |x^(2)+4x+3|+2x+5=0

    Text Solution

    |

  10. For a gt0, determine all the roots of the equations x^(2)-2a|x-a|-3a...

    Text Solution

    |

  11. How many five -digit numbers divisible by 3 can do formed using the d...

    Text Solution

    |

  12. How many five-digit telephone numbers with pairwise distinct digits ca...

    Text Solution

    |

  13. Five speakers A,B,C,D and E will speark at a meeting. In how many ways...

    Text Solution

    |

  14. If z(1)=3i and z(2)=-1-i , where i=sqrt(-1) find the value of arg ((z(...

    Text Solution

    |

  15. Show that the number of solutions of equations |x|^(2)-3|x|+2=0 is 4.

    Text Solution

    |

  16. Show that (1)/(2)[(x-y)^(4)+(y-z)^(4)+(z-x)^(4)] is perfect square.

    Text Solution

    |

  17. In an arithmetic progression of n terms ( n is even) , the two middle ...

    Text Solution

    |

  18. In an A.P. fo n terms (n is even), the two middle terms are (alpha- be...

    Text Solution

    |

  19. Prove that the ineuations (2x+1)/(7x-1) gt 5 and (x+7)/(x-8)gt2 have n...

    Text Solution

    |

  20. If the argument of (z-a)(barz-b) is equal to that of ((sqrt(3)+i)(1+sq...

    Text Solution

    |