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Sequence Limit (Posted on 20130924) 

Consider this infinite sequence:
a, b, c, (a+b+c)/3, (a+4b+4c)/9, (4a+7b+16c)/27 .....
where, each of a, b and c is a real number and, each term after the third is the arithmetic mean of the three previous terms.
Determine the limit of the sequence in terms a, b and c.
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