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  • Sequences

    Anonymous Christian
    Sep 5, 2014
    MATH, Math Olympiad
    Comments Off on Sequences

    Question

    Find in terms of n, the n th term of the sequence:
    1/3 , 2/5 , 3/7, 4/9 , 5/11 , . . .

    Answer

    Here is a neat way to look at it…

    Lets count for n = 1,2,3 etc. As we “count” we “observe” how this counting “relates” to the “pattern of the numbers given”.

    Consider the “numerator” and “denominator” pattern of numbers separately.

    For the “numerator”, we have :
    n = 1 ,Numerator value : 1
    n = 2 ,Numerator value : 2
    n = 3 ,Numerator value : 3
    n = 4 ,Numerator value : 4
    n = 5 ,Numerator value : 5
    See the pattern?
    …n = m, Numerator Value : m.

    Now consider the “denominator” values in the similar manner.
    n = 1 ,Denominator value : 3 = 2(1) + 1
    n = 2 ,Denominator value : 5 = 2(2) + 1
    n = 3 ,Denominator value : 7 = 2(3) +1
    n = 4 ,Denominator value : 9 = 2(4) +1
    n = 5 ,Denominator value : 11 = 2(5) +1
    See the pattern?
    …n = m, Numerator Value : 2(m) + 1.

    Hence “combining” our observations above,
    The “nth term” will be = (n)/[ 2(n) + 1]

    That’s it!

anonymous-christian

Jonathan Ramachandran is founder at AnonymousChristian.org which serves as a Christian Blog discussing the Greater Hope of Biblical Christian in Christ Alone. He is also an IMO (International Math Coach) and a featuring Guitarist for many bands.

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