Home
Class 12
MATHS
The nature of the S(n)=3n^(2)+5n series ...

The nature of the `S_(n)=3n^(2)+5n` series is

A

AP

B

GP

C

HP

D

AGP

Text Solution

Verified by Experts

The correct Answer is:
A
`:. S_(n)=3n^(2)+5n`
`:. T_(n)=S_(n)-S_(n-1)`
`=(3n^(2)+5n)-[3(n-1)^(2)+5(n-1)]`
`=3(2n-1)+5=6n+2`
The nth term is a linear function in n. Hence, sequence must be an AP.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|5 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|11 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

In an arithmetic series, if S_(n)=3n^(2)+2n , find the first three terms.

If the sum of n terms of an A.P. is S_n=3n^2+5n . Write its common difference.

Suppose a series of n terms given by S_(n)=t_(1)+t_(2)+t_(3)+ . . . . +t_(n) then S_(n-1)=t_(1)+t_(2)+t_(3)+ . . . . +t_(n-1),nge1 subtracting we get S_(n)-S_(n-1)=t_(n),nge2 surther if we put n=1 is the first sum then S_(1)=t_(1) thus w can write t_(n)=S_(n)-S_(n-1),nge2 and t_(1)=S_(1) Q. The sum of n terms of a series is a.2^(n)-b . where a and b are constant then the series is

If the sum of n terms of a sequence is given by S_(n)=3n^(2)-2nAA n in N , then its 10th term is

The sum of n terms of an A.P. series is (n^(2) + 2n) for all values of n. Find the first 3 terms of the series:

For all natural number of n, 2^(2n).3^(2n)-1-35n is divisible by

Prove by induction that the sum S_n=n^3+3n^2+5n+3 is divisible by 3 for all n in Ndot

Find the sum of 'n' terms of the series whose n^(th) term is t_(n) = 3n^(2) + 2n .

If S_(n) denotes sum of first n tem of a series and if S_(n+2)-S_(n)=n^(2) then S_(20) is ("given that" T_(1)+T_(2)=0)

The value of lim_(n to oo) (2n^(2) - 3n + 1)/(5n^(2) + 4n + 2) equals

ARIHANT MATHS ENGLISH-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The nature of the S(n)=3n^(2)+5n series is

    Text Solution

    |

  2. Let a,b,c be in A.P. and |a|lt1,|b|lt1|c|lt1.ifx=1+a+a^(2)+ . . . ."to...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. If a1, a2, a3, be terms of an A.P. and (a1+a2+.....+ap)/(a1+a2+.....+...

    Text Solution

    |

  5. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

    Text Solution

    |

  6. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

    Text Solution

    |

  7. Let Vr denote the sum of the first r terms of an arithmetic progressio...

    Text Solution

    |

  8. Let V(r) denote the sum of the first r terms of an arithmetic progress...

    Text Solution

    |

  9. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

    Text Solution

    |

  10. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  11. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

    Text Solution

    |

  12. In a G.P of positive terms if any term is equal to the sum of the next...

    Text Solution

    |

  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

    Text Solution

    |

  14. The first two terms of a geometric progression add up to 12. The sum o...

    Text Solution

    |

  15. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

    Text Solution

    |

  16. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

    Text Solution

    |

  17. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

    Text Solution

    |

  18. Let a1, a2, a3, ,a(11) be real numbers satisfying a1=15 , 27-2a2>0 a ...

    Text Solution

    |

  19. A person is to count 4500 currency notes. Let an denote the number of ...

    Text Solution

    |

  20. The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1,a^8 ...

    Text Solution

    |

  21. A man saves ₹ 200 in each of the first three months of his servies.In ...

    Text Solution

    |