Home
Class 11
MATHS
If the sequence an is A.P., show that a(...

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

Text Solution

Verified by Experts

It is given that the sequence `a_n` is an A.P.
`therefore a_{n}=a+(n-1) d ldots . . { (i) }`
Similarly from (i)
`a_{m+n}=a+(m+n-1) d ldots . .( { ii } `
...
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 a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_n))

Find the indicated terms in each of the following sequences whose nth terms are: a_(n)=5_(n)-4;a_(12) and a_(15)a_(n)=(3n-2)/(4n+5);a+7 and a_(8)a_(n)=n(n-1);a_(5)anda_(8)a_(n)=(n-1)(2-n)3+n);a_(1),a_(2),a_(3)a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)

Find the indicated terms in each of the following sequences whose n^(th) terms are a_(n) = (a_(n-1))/(n^(2)) , (n ge 2) , a_(1) =3 , a_(2) , a_(3)

If a_(1), a_(2), a_(3),........, a_(n) ,... are in A.P. such that a_(4) - a_(7) + a_(10) = m , then the sum of first 13 terms of this A.P., is:

If the sequence a_(1),a_(2),a_(3),dots a_(n),.... forms an A.P.then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)+...+a_(4)^(2)=(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))

The fibonacct sequence is defined by 1=a_(1) = a_(2) and a_(n-1) + a_( n-1) , n gt 1 Find (a_(n+1))/(a_(n)) " for " n =1 ,2,34,5,

The nth term of a sequence is given by a_(n)=2n^(2)+n+1. Show that it is not an A.P.

RD SHARMA-ARITHMETIC PROGRESSIONS-Solved Examples And Exercises
  1. Find: 18th term of the A.P. sqrt(2),\ 3sqrt(2),\ 5sqrt(2) ddot

    Text Solution

    |

  2. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

    Text Solution

    |

  3. If the sequence an is A.P., show that a(m+n)+a(m-n)=2amdot\

    Text Solution

    |

  4. Which term of the A.P. 3,8,13… is 248?

    Text Solution

    |

  5. Which term of the A.P. 84,80,76… is 0?

    Text Solution

    |

  6. Which term of the A.P. 4,9,14… is 254?

    Text Solution

    |

  7. Is 68 as term of the A.P. 7,10,13,…?

    Text Solution

    |

  8. Is 302 a term of the A.P. 3,8,13,…?

    Text Solution

    |

  9. Which term of the sequence 24 ,\ 23 1/4,\ 22 1/2,\ 21 3/4 is the first...

    Text Solution

    |

  10. Which term of the sequence 12+8i ,\ 11+6i ,\ 10+4i ,... is (a) purely ...

    Text Solution

    |

  11. How many terms are there in the A.P. 7,10,13,…43?

    Text Solution

    |

  12. How many terms are there in the A.P. -1,\ -5/6,\ -2/3,-1/2,\ ,(10)/3?

    Text Solution

    |

  13. The first term of an AP. is 5, the common difference is 3 and the last...

    Text Solution

    |

  14. The 6th and 17th terms of an A.P. are 19 and 41 respectively, find t...

    Text Solution

    |

  15. If 10 times the 10th term of an A.P. is equal to 15 times the 15th t...

    Text Solution

    |

  16. The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find...

    Text Solution

    |

  17. In certain A.P. the 24th term is twice the 10th term. Prove that th...

    Text Solution

    |

  18. If the nth term of the A.P. 9,7,5,... is same as the nth term of the A...

    Text Solution

    |

  19. Find the 12th term from the end of the following arithmetic progres...

    Text Solution

    |

  20. Find the 12th term from the end of the following arithmetic progres...

    Text Solution

    |