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Math Help - Problem Involving Arithmetic progression

  1. #1
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    Problem Involving Arithmetic progression

    The first two terms of an arithmetic progression are 21 and 18.If the sum of the first n th term is -24.Find the value of n
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  2. #2
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    If you know the the first two terms, you know the initial term and the common difference. This Wikipedia article then gives you the formula for the sum of n terms, so you have to solve the equation for n.
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  3. #3
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    The formula for a sum of a finite arithmetic series is:

    \frac{n(2a_1+d(n-1))}{2}

    In this formula, a_1 is the first term. n is the number of terms. d is the common difference (the rate at which the series progresses).

    We know that the first term is 21, and we know that the common difference is -3, and that the sum of this series is -24.

    Therefore, we have:

    \frac{n(42-3(n-1))}{2}=-24

    now we solve for n:

    n(42-3n+3)=-48

    42n-3n^2+3n=-48

    45n=3n^2-48

    divide by three to get:

    15n=n^2-16

    n^2-15n-16=0

    (n-16)(n+1)=0

    Therefore:

    n-16=0 or n+1=0

    n=16 or n=-1

    Since we cant have a negative number of terms, -1 is not a valid answer. Thus, we have :

    n=16
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  4. #4
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    Quote Originally Posted by mastermin346 View Post
    The first two terms of an arithmetic progression are 21 and 18.

    If the sum of the first n th term is -24, find the value of n
    Can you just confirm that that is the "sum of the first n terms"
    rather than the "sum of the first and nth terms" ?
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