Home
Class 11
MATHS
If the sum of n terms of an A.P. is 3n^(...

If the sum of n terms of an A.P. is `3n^(2)+5n` and its mth term is 164, find the value of m.

Text Solution

Verified by Experts

Here, we are given,
`n/2(2a+((n-1)d) = 3n^2+5n`
`(2a-d)+nd = 6n+10`
`d = 6 and 2a-d=10`
`d=6 and a =8`
Now, `m^(th)` term `= a+(m-1)d = 164`
`=>8+6(m-1) = 164`
`=>6(m-1) = 156`
...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.3|32 Videos

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.1|14 Videos

  • SEQUENCES AND SERIES

    NCERT|Exercise EXERCISE 9.4|10 Videos

  • RELATIONS AND FUNCTIONS

    NCERT|Exercise EXERCISE 2.3|5 Videos

  • SETS

    NCERT|Exercise EXERCISE 1.5|7 Videos

Similar Questions

Explore conceptually related problems

The sum of n terms of AP is 3n^(2)+5n. and its nth term is 164. find the value of n.

The sum of first n terms of an A.P.is 5n^(2)+3n If its mth term is 168,(i) Find the value of m (ii) Find the 20th term of this AP

The sum of n terms of an A.P. is n^(2) + 3n . Find its 20th term.

If the sum of n terms of an A.P is 2n+3n^(2) , find the r^(th) term

If sum of n terms of an A.P. is n^(2)+13 , find its 13^(th) term.

If the sum of n terms of an AP is n^2-2n then find its n^(th) term

The sum of first n terms of an A.P. is 5n^(2) + 3n . If the nth term is 168, find the value of n. Also find the 20th term of the A.P.

The sum of n terms of an AP is 3n^2+5n ,then find its 16th term.

If the sum of first n terms of an A.P. is 3n^(2)-2n , then its 19th term is

If sum of n terms of an AP is 3n^2+n . Find its 10^(th) term.

NCERT-SEQUENCES AND SERIES-EXERCISE 9.2
  1. Sum of the first p, q and r terms of an A.P are a, b and c, respectiv...

    Text Solution

    |

  2. Insert five numbers between 8 and 26 such that the resulting sequence...

    Text Solution

    |

  3. A mail starts repaying a loan as first instalment of Rs. 100. If he i...

    Text Solution

    |

  4. The difference between any two consecutive interior angles of a polyg...

    Text Solution

    |

  5. Between 1 and 31, m numbers have been inserted in such a way that the...

    Text Solution

    |

  6. If the sum of first p terms of an A.P. is equal to the sum of the fir...

    Text Solution

    |

  7. If the sum of n terms of an A.P. is 3n^(2)+5n and its mth term is 164,...

    Text Solution

    |

  8. The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2). Show...

    Text Solution

    |

  9. If (a^n+b^n)/(a^(n-1)+b^(n-1))is the A.M. between a and b, then find t...

    Text Solution

    |

  10. If the sum of n terms of an A.P. is (p n+q n^2), where p and q are co...

    Text Solution

    |

  11. The sums of n terms of two arithmetic progressions are in the ratio 5...

    Text Solution

    |

  12. If the sum of a certain number of terms of the A.P. 25, 22, 19.... is...

    Text Solution

    |

  13. Find the sum to n terms of the A.P., whose k^(t h)term is 5k + 1.

    Text Solution

    |

  14. How many terms of the A.P. 6, -(11)/2,-5,...........are needed to gi...

    Text Solution

    |

  15. In an A.P., if p^(t h)term is 1/qand q^(t h)term is 1/p, prove that t...

    Text Solution

    |

  16. Find the sum of all natural numbers lying between 100 and 1000, which...

    Text Solution

    |

  17. In an A.P., the first term is 2 and the sum of the first five terms i...

    Text Solution

    |

  18. Find the sum of odd integers from 1 to 2001.

    Text Solution

    |