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Math Help - Arithmetic progression

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    Arithmetic progression

    The first and third term of arithmetic progression are x and y respectively.Find the sixteenth term in term of x and y.
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    Quote Originally Posted by mastermin346 View Post
    The first and third term of arithmetic progression are x and y respectively.Find the sixteenth term in term of x and y.
    The values of the arithmetic progression are calculated by

    a_n=a_1+(n-1)\cdot d

    with

    d = a_{n+1} - a_n

    In your case d = \frac{y-x}2.

    Plug in the values you know:

    n = 16
    a_1 = x
    a_3 = y

    and calculate a_{16}.
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    Quote Originally Posted by mastermin346 View Post
    The first and third term of arithmetic progression are x and y respectively.Find the sixteenth term in term of x and y.
     x + (x+d) + (x+2d) + (x+3d) + ... (x + 15d)
    where  d is the constant difference between each successive term.

    In our case, we are told that the third term is y. Thus,  x+2d = y .

    So,  d = \frac{y-x}{2}


     a_1 = x

     a_2 = x + \frac{y-x}{2} = \frac{2x}{2} + \frac{y-x}{2} =<br />
\frac{2x+y-x}{2} = \frac{x+y}{2}<br />

     a_3 = \frac{x+y}{2} + \frac{y-x}{2}= \frac{2y}{2} = y
    ...
    ...
    ...


     a_{16} = x + 15d = x + 15\big{(}\frac{y-x}{2}\big{)}
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    Quote Originally Posted by mastermin346 View Post
    The first and third term of arithmetic progression are x and y respectively.Find the sixteenth term in term of x and y.
    y = x + 2d \Rightarrow d = \frac{y - x}{2}. And the first term is x.

    You now have everything necessary to do anything you want, including finding the sixteenth term.
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