Home
Class 9
MATHS
If the first terms, second term and the ...

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

Promotional Banner

Topper's Solved these Questions

  • PROGRESSION

    KALYANI PUBLICATION|Exercise EXERCISE|249 Videos

  • MATHEMATICAL LOGIC

    KALYANI PUBLICATION|Exercise EXERCISE|290 Videos

  • SYSTEM OF NUMERATION

    KALYANI PUBLICATION|Exercise EXERCISE|101 Videos

Similar Questions

Explore conceptually related problems

If the first,second and last term of an AP are a,b and 2a respectively,its sum is

The first term and last term of an A.P. are respectively 1 and 157. If the sum is 3160 find the number of terms.

The fifth and ninth terms of an A.P. are respectively -15 and -13. Find the sum of first ten terms.

If the mth term and nth term of an A.P. are respectively n and m show that the (m + n)th term is zero and pth term is m + n-p .

The first term and common difference of an A.P. are respectively 4 and 2. If the sum up to n terms is 88, find n.

4th term, 10th term and nth term of an A.P. are 7, 25, 58 respectively. Find 1st term, C.D. and the value of n.

The first term and common difference of an A.P. are respectively -2 and -4. If the sum upto n terms is —288, find n.

The first term and the last term of an A.P. are 2 and 29, respectively. If the sum of the series is 155, find the number of terms and common difference.

In an A.P. the pth and qth terms are respectively a and b. Show that the sum of first p + q terms is (p+q)/2{(a+b)+(a-b)/(p-q)} .

The fourth term and eighth term of an A.P. are 2 and 10 respectively. Determine the A.P. and its 11th term.

KALYANI PUBLICATION-PROGRESSION-EXERCISE
  1. The ratio of sum of the first n terms of two series in A.P is (3n + 8)...

    Text Solution

    |

  2. In an A.P. the pth and qth terms are respectively a and b. Show that t...

    Text Solution

    |

  3. If the first terms, second term and the last term of an A.P. are respe...

    Text Solution

    |

  4. The sum of first n terms of an A.P. is Sn.If Sn=n^2p and Sm=m^2p(mn...

    Text Solution

    |

  5. The first term of an A.P. is a. If sum of first p terms is zero, pro...

    Text Solution

    |

  6. The sum of first P terms of an A.P. is equal to that of the first Q te...

    Text Solution

    |

  7. Find the sum of all odd numbers lying between 12 and 90.

    Text Solution

    |

  8. Determine the sum of the numbers lying between 100 and 500 which are d...

    Text Solution

    |

  9. Find the sum of all numbers lying between 1 and 100 which are divisibl...

    Text Solution

    |

  10. Determine the sum of the numbers lying between 100 and 200 which are n...

    Text Solution

    |

  11. Determine the sum of following series upto n terms. 1.2+2.3+3.4+…….

    Text Solution

    |

  12. Determine the sum of following series upto n terms. 1.1+2.3+3.5+…….

    Text Solution

    |

  13. Determine the sum of following series upto n terms. 2.1+3.3+4.5+…….

    Text Solution

    |

  14. Determine the sum of following series upto n terms. 3.8+6.11+9.14+……...

    Text Solution

    |

  15. Determine the sum of following series upto n terms. 1.3+2.4+3.5+…….

    Text Solution

    |

  16. Determine the sum of following series upto n terms. 1.3+5.7+9.11+…….

    Text Solution

    |

  17. Determine the sum of following series upto n terms. (3^2-2^2)+(5^2-4...

    Text Solution

    |

  18. Determine the sum of following series upto n terms. (1^2-2^2)+(3^2-4...

    Text Solution

    |

  19. Determine the sum of following series upto n terms. 1.2^2+2.3^2+3.4^...

    Text Solution

    |

  20. Determine the sum of following series upto n terms. 1+(1+2)+(1+2+3)+...

    Text Solution

    |