Home
Class 11
MATHS
The first , second and the last terms of...

The first , second and the last terms of an A.P. are `a ,b , c` respectively. Prove that the sum is `((a+c)(b+c-2a))/(2(b-a))` .

Text Solution

AI Generated Solution

To prove that the sum of the first, second, and last terms of an A.P. (Arithmetic Progression) is given by the formula \(\frac{(a+c)(b+c-2a)}{2(b-a)}\), we will follow these steps: ### Step 1: Identify the terms Given: - First term \(a\) - Second term \(b\) - Last term \(c\) ...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    RD SHARMA|Exercise Solved Examples And Exercises|228 Videos

Similar Questions

Explore conceptually related problems

If the first, second and the last terms of an A.P. are a,b,c respectively, then the sum of the A.P. is

The first,second and middle terms of an AP are a,b,c respectively.Their sum is

If the first second and last terms of an A.P.are a,b and 2a respectively,then its sum is

If the first second and last term of an A.P.are a,b, and 2a respectively then its sum is (ab)/(2(b-a)) b.(ab)/(b-a) c.(3ab)/(3(b-a)) d.none of these

If the first, second and last term of an A.P. are a ,\ b and 2a respectively, its sum is (a b)/(2(b-a)) (b) (a b)/(b-a) (c) (3a b)/(2(b-a)) (d) none of these

If the first second and third term of AP are a,b and 2 a respectively.Then the sum of the AP is

If the first, second and last terms of an arithmetic series are a,b and c respectively , then the number of terms is

Sum of the first p,q and r terms of an A.P are a,b and c,respectively.Prove that quad (a)/(p)(q-r)+(b)/(q)(r-p)+(c)/(r)(p-q)=0

RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. The sums of n terms of three arithmetical progressions are S1, S2and ...

    Text Solution

    |

  2. If in an A.P. the sum of m terms is equal of n and the sum of n ter...

    Text Solution

    |

  3. The first , second and the last terms of an A.P. are a ,b , c respect...

    Text Solution

    |

  4. If (3+5+7+ u p tont e r m s)/(5+8+113 u p to10t e r m s)=7, then find...

    Text Solution

    |

  5. In a factory, 150 workers were engaged to finish a piece of work in a ...

    Text Solution

    |

  6. Prove that the sum of n arithmetic means between two numbers in n ti...

    Text Solution

    |

  7. If a ,b ,c are in A.P., then prove that: (a-c)^2=4(b^2-a c), a^3+...

    Text Solution

    |

  8. If a^2(b+c),b^2(c+a),c^2(a+b), are in A.P. show that either a ,b ,c ar...

    Text Solution

    |

  9. If n arithemetic means are inserted between 20 and 80 such tht the r...

    Text Solution

    |

  10. Along a road lie an odd number of stones placed at intervals of 10 met...

    Text Solution

    |

  11. A carpenter was hired to build 192 window frames. The first day he mad...

    Text Solution

    |

  12. In a potato race 20 potatoes are placed in a line at intervals of 4m e...

    Text Solution

    |

  13. We know that the sum of the interior angles of a triangle is180^0 . S...

    Text Solution

    |

  14. If S1 be the sum of (2n+1) term of an A.P. and S2 be the sum of its od...

    Text Solution

    |

  15. Divide 32 into four parts which are in A.P. such that the product of ...

    Text Solution

    |

  16. If theta1,theta2,theta3, ,thetan are in AP, whose common difference ...

    Text Solution

    |

  17. If (m+1) term of an A.P. is twice the(n+1) th term, prove that (3m+1) ...

    Text Solution

    |

  18. If a1,a2,a3, ,an are in A.P. with common difference d(w h e r ed!=0), ...

    Text Solution

    |

  19. If an A.P. is such that (a4)/(a7)=2/7, find (a6)/(a8) .

    Text Solution

    |

  20. The 4th term of an A.P. is three times the first and the 7th term e...

    Text Solution

    |