Home
Class 11
MATHS
Show that the sequence is an A.P. if its...

Show that the sequence is an A.P. if its nth term is linear expression in `n` and in such a case the common difference is equal to the coefficient of `ndot`

Text Solution

Verified by Experts

The correct Answer is:
N/a

Let nth term of a progression be
`T_(n)=an+b`
where a and b are constants.
`T_(n-1)=a(n-1)+b=an-a+b`
`"and "T_(n)-T_(n-1)=(an+b)-(an-a+b)=a`
which does not depend on 'n' so it is constant.
`rArr` Given progression is an arithmetic progression.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9A|4 Videos
  • SEQUENCE AND SERIES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 9B|18 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

Show that a sequence is an AdotPdot if its n t h term is a linear expression in n and in such a case the common difference is equal to the coefficient of n .

Write the common difference of an A.P. whose nth term is x n+ydot

Find the A.P. whose nth term is 2n-3.

Show that the sequence 9,12,15,18,... is an A.P. Find its 16th term and the general term.

Show that the sequence 9,12,15,18,... is an A.P. Find its 16th term and the general term.

Show that the sequence 9,12,15,18,... is an A.P. Find its 16th term and the general term.

If the first term of an A.P. is a and n t h term is b , then its common difference is

If gerneral term of an A.P. is 2n + 5 , then its common difference is

Show that the sequence 9, 12, 15, 18, ... is an A.P. Find its 16th term and the general term.

In an A.P. first term is 5, last term is 45 and sum = 400 . Find the no. of terms and common difference of A.P.

NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Miscellaneous Exercise
  1. Show that the sequence is an A.P. if its nth term is linear expression...

    Text Solution

    |

  2. 32. Show that the sum of (m+n)^(th) and (m-n)^(th) terms of an A.P. is...

    Text Solution

    |

  3. The sum of three numbers in A.P. is 27, and their product is 504, find...

    Text Solution

    |

  4. Let the sum of n, 2n, 3n terms of an A.P. be S1,S2and S3, respectively...

    Text Solution

    |

  5. Find the sum of all numbers between 200 and 400 which are divisible...

    Text Solution

    |

  6. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

    Text Solution

    |

  7. Find the sum of all two digit numbers which when divided by 4, yiel...

    Text Solution

    |

  8. If f is a function satisfying f(x+y)=f(x)f(y)for all x ,y in Xsuch t...

    Text Solution

    |

  9. The sum of some terms of G. P. is 315 whose first term and the comm...

    Text Solution

    |

  10. The first term of a G.P. is 1. The sum of the third and fifth terms is...

    Text Solution

    |

  11. The sum of three numbers m GP is 56. If we subtract 1.7,21 from the...

    Text Solution

    |

  12. A G.P. consists of an even number of terms. If the sum of all the t...

    Text Solution

    |

  13. The sum of the first four terms of an A.P. is 56. The sum of the la...

    Text Solution

    |

  14. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+dx)/(c-dx)(x!=0),then show that...

    Text Solution

    |

  15. LetS be the sum, P the product, and R the sum of reciprocals of n term...

    Text Solution

    |

  16. The p^(t h),q^(t h)and r^(t h)terms of an A.P. are a, b, c, respectiv...

    Text Solution

    |

  17. If a (1/b+1/c),b(1/c+1/a),c(1/a+1/b)are in A.P., prove that a, b, c a...

    Text Solution

    |

  18. If a, b, c, d are in G.P., prove that (a^n+b^n),(b^n+c^n),(c^n+a^n)ar...

    Text Solution

    |

  19. If a and b are the roots of x^2-3x+p=0and c, d are roots of x^2-12 x+...

    Text Solution

    |

  20. The ratio of the A.M. and G.M. of two positive numbers a and b, is m ...

    Text Solution

    |

  21. If a ,\ b ,\ c are in A.P. b ,\ c ,\ d are in G.P. and 1/c ,1/d ,1/e a...

    Text Solution

    |