Home
Class 11
MATHS
In an A.P., prove that : T(m+n) + T(m-n)...

In an A.P., prove that : `T_(m+n) + T_(m-n) = 2*T_(m)`

Text Solution

AI Generated Solution

To prove that \( T_{m+n} + T_{m-n} = 2T_m \) in an arithmetic progression (A.P.), we will follow these steps: ### Step 1: Write the general term of an A.P. The general term \( T_n \) of an A.P. can be expressed as: \[ T_n = a + (n-1)d \] where \( a \) is the first term and \( d \) is the common difference. ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9C|26 Videos
  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9D|11 Videos
  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9A|4 Videos
  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|12 Videos
  • SETS

    NAGEEN PRAKASHAN ENGLISH|Exercise MISC Exercise|16 Videos

Similar Questions

Explore conceptually related problems

For an A.P. show that t _(m) + t _(2n + m) = 2 t _(m +n)

For an A.P., show that (m +n)th term + (m-n) term =2 xx m th term

If the sequence a_n is A.P., show that a_(m+n)+a_(m-n)=2a_mdot\

The sum of m terms and n terms of an A.P. ae equal. Prove that the sum of (m+n) terms will be zero. Given that mnen.

If in an A.P. the sum of m terms is equal of n and the sum of n terms is equal to m , then prove that the sum of -(m+n) terms is (m+n) .

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot

Let {t_(n)} is an A.P If t_(1) = 20 , t_(p) = q , t_(q) = p , find the value of m such that sum of the first m terms of the A.P is zero .

Let T be the r th term of an A.P. whose first term is a and conmon difference is d . If for some positive integers m ,n, T_(n)= (1)/(m) , T_(m) = (1)/(n) then (a – d) equals

In an A.P,the sum of m terms of an AP is n and sum of n terms of AP is m,then prove that sum of (m+n) terms of AP is-(m+n)

If in an A.P. the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9B
  1. (a) The nth term of a progression is (3n + 5). Prove that this progres...

    Text Solution

    |

  2. (a) Find the 10th term of the progression 1 + 3 + 5 +7+ ... (b) Find...

    Text Solution

    |

  3. (a) Which term of the progression 4 + 8 + 12 + ... is 76 ? (b) Which...

    Text Solution

    |

  4. (a) Find the 16th term from the end of the progression 3 + 6 + 9 + ......

    Text Solution

    |

  5. (a) How many numbers of two digits are divisible by 3 ? (b) How man...

    Text Solution

    |

  6. (a) Find the value of 'x if x + 1, 2x + 1 and x + 1 are in A.P. Also f...

    Text Solution

    |

  7. (a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find...

    Text Solution

    |

  8. Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prov...

    Text Solution

    |

  9. The 12th term of an A.P. is 14 more than the 5th term. The sum of thes...

    Text Solution

    |

  10. (a) Is 303, a term of the progression 5, 10, 15, ... ? (b) Is 38, a...

    Text Solution

    |

  11. Prove that the sum of nth term from the beginning and nth term from th...

    Text Solution

    |

  12. In an A.P., prove that : T(m+n) + T(m-n) = 2*T(m)

    Text Solution

    |

  13. (i) 10 times the 10th term and 15 times the 15th term of an A.P. are e...

    Text Solution

    |

  14. Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pur...

    Text Solution

    |

  15. (a) Which term of the progression 10,9(1)/(3),8 (2)/(3),...is the firs...

    Text Solution

    |

  16. Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... are ...

    Text Solution

    |

  17. If a(1),a(2),….a(n) are in arthimatic progression, where a(i)gt0 for a...

    Text Solution

    |

  18. If the numbers a , b , c , d , e form an A.P. , then find the value of...

    Text Solution

    |