Results 1 to 6 of 6

Math Help - problem on A.P/G.P

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    11

    problem on A.P/G.P

    Please solve the problem for me
    Find the sum of the series
    3+7+14+27+52+...................up to nth terms
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by somnath6088 View Post
    Please solve the problem for me
    Find the sum of the series
    3+7+14+27+52+...................up to nth terms
    The nth term in the series is given by the recurrence relation a_n = 2 a_{n-1} - n + 3 with a_1 = 3. This does not define an Arithmetic Sequence or a Geometric Sequence.

    So I don't know why you would imply the series is arithmetic or geometric in your descriptive title of the problem.

    Once you've got the nth term of the series in terms of n, you'll have more luck finding the value of the series.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    11
    sorry.
    the problem is
    1+3+7+14+27+52+........up to nth terms.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    Can you see the pattern?

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member wingless's Avatar
    Joined
    Dec 2007
    From
    Istanbul
    Posts
    585
    3 + 7 + 14 + 27 + 52 + ...

    a_n = 3\cdot 2^n + n (starting from a_0)

    S_n = \sum_{k=0}^{n}3\cdot 2^k + k

    S_n = 3\sum_{k=0}^{n}2^k +\sum_{k=0}^{n}k

    S_n =  3\cdot (2^{n+1}-1) + \frac{n(n+1)}{2}

    You can add +1 to S_n if you want to sum 1+3+7+14+27+...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by mr fantastic View Post
    The nth term in the series is given by the recurrence relation a_n = 2 a_{n-1} - n + 3 with a_1 = 3. This does not define an Arithmetic Sequence or a Geometric Sequence.

    So I don't know why you would imply the series is arithmetic or geometric in your descriptive title of the problem.

    Once you've got the nth term of the series in terms of n, you'll have more luck finding the value of the series.
    The nth term in the series (the original, not the revised) is \frac{3}{2} \, (2^n) + n - 1 (starting from n = 1). Others will benefit from knowing the correct series and might have more to say. I'll just give this reply to complement my first.

    And in fact, you can still use this result. Use it to get the sum and then just add 1 to the result.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum