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Number Sequences

  1. May 18, 2014 #1
    Hi all

    I'm studying sequences and series, the problem I am having is this:-

    Given the sequence 8 11 14

    Find the Nth Term.

    I have worked out the nth term to be 3N+5, so if I wanted to find the 4th term it would be 3*4+5 = 17.

    The problem is that I have come across the following formula:-

    a+(n-1)d where a = 1st term, N is the Nth term, d common difference.

    If I plug in the values into the above formula I get:-
    8+(4-1)*3 = 17

    I get the same result?? the problem I am having is that I do not understand how the two are related?

    Can someone explain??
  2. jcsd
  3. May 18, 2014 #2


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    Science Advisor
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    Gold Member

    Try expanding the term in parentheses and writing the result in the form A*n+B.
  4. May 18, 2014 #3


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    Homework Helper

    Our sequence is
    a, a+d, a+2d, ...

    which is equivalent to

    a+0d, a+1d, a+2d, ...

    So what we have is:
    1st = a+0d
    2nd = a+1d
    3rd = a+2d
    nth = a+(n-1)d

    So in order to use a formula that's of this form, we need to make our 1st term (n=1) have a value of 0, n=2 have a value of 1... our nth value have a value of (n-1).

    Hence a+(n-1)d does just this.
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