Home
Class 12
MATHS
Determine whether (tn) is an arithmetic ...

Determine whether `(t_n)` is an arithmetic sequence if: `t_n=an^2+b`

Text Solution

Verified by Experts

`t_nan^2+brArrt_(n+1)=a(n+1)^2+b`
`thereforet_(n+1)-t_n=a[n+1)^2-n^2]+b-b=a(2n+1)` (does not independent of n)
`therefore(t_n)` is not an arithmetic sequence.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|106 Videos

  • SETS

    MBD PUBLICATION|Exercise QUESTION BANK|110 Videos

Similar Questions

Explore conceptually related problems

Determine whether (t_n) is an arithmetic sequence if: t_n=an+b

For each binary operation defined below, determine whether * is the commutative or not. On N defined a*b =a+b +2 .

Determine whether the solution set is finite or infinite or empty: x lt 1000, x in N

Determine whether the following operation on the set R is associative and commutative a ** b = (a + b)/2 for all a, b in R .

State whether the following statements are True (T) or False (F): The two factors that determine whether the lens is converging or diverging are The refractive index of the medium (mu_2) of which the lens is made of and the refractive index of the medium (mu_1) in which the lens is immersed.

For an arithmetic sequence (t_n)t_p=q,t_q=p,(pneq), find t_n .

Determine whether a**b ="min" {a,b} "on" N operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

Determine if the set A=x:x is a prime number } is a proper subset of the set B={2n-1:n=1,2,3…..}

For each binary operation defined below, determine whether * is the commutative or not. On R defined a *b = a + 4b^(2) .

Determine whether a**b =a^2 +b^2 "on" N operations as defined by * are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.

MBD PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. Determine whether (tn) is an arithmetic sequence if: tn=an^2+bn

    Text Solution

    |

  2. Determine whether(tn) is an arithmetic sequence if: tn=an+b

    Text Solution

    |

  3. Determine whether (tn) is an arithmetic sequence if: tn=an^2+b

    Text Solution

    |

  4. If a geometic series converges which of the following is true about it...

    Text Solution

    |

  5. If an arithmetic series sumtn converges, which of the following is tru...

    Text Solution

    |

  6. Which of the following is an arithmetico geometric series ?

    Text Solution

    |

  7. For an arithmetic sequence (tn)tp=q,tq=p,(pneq), find tn.

    Text Solution

    |

  8. For an arithmetic series suman, Sp=qandSq=p(pneq)find S(p+q)

    Text Solution

    |

  9. The sum of a geometric series is 3. the series of squares of its terms...

    Text Solution

    |

  10. The sum of a geometric series is 14, and the series of cubes of its te...

    Text Solution

    |

  11. Find the sum as directed.1+2a+3a^2+4a^3+.... (first n terms (ane1))

    Text Solution

    |

  12. Find the sum as directed.1+(1+x)y+(1+x+x^2)y^2+... (to infinity)

    Text Solution

    |

  13. Find the sum as directed.1+3/5+7/25+15/125+31/625+... (to infinity)

    Text Solution

    |

  14. Find the sum as directed.1+4x+8x^2+13x^3+19x^4+... (to infinity) Assum...

    Text Solution

    |

  15. Find the sum as directed.3.2+5.2^2+7.2^3+.... (first n terms)

    Text Solution

    |

  16. Find the sum of the infinite series. 1/(1.2)+1/(2.3)+1/(3.4)+...

    Text Solution

    |

  17. Find the sum of the infinite series.1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...

    Text Solution

    |

  18. Find the sum of the infinite series.1/(2.5.8)+1/(5.8.11)+1/(8.11.14)+....

    Text Solution

    |

  19. Find the sum of the infinite series.3/(1^(2).2^(2))+5/(2^(2).3^(2))+7/...

    Text Solution

    |

  20. Find the sum of the infinite series. 1/(1.5)+1/(3.7)+1/(5.9)+...

    Text Solution

    |