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1/6,1/3,1/2,2/3,___, ___ (hint: rewrite each fraction so they all have a common deniminator of 6) (write the next 2 terms and write the rule)

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Answer:


\textsf{The next two terms are:}\quad (5)/(6)\;\textsf{and}\;1


\textsf{The rule for the $n$th term is:}\quad a_n=(n)/(6)

Explanation:

Given sequence:


(1)/(6),\;\;(1)/(3),\;\;(1)/(2),\;\;(2)/(3),\;...

To find the next two terms in the given sequence, begin by rewriting each fraction so that they all have a common denominator of 6. To achieve this, multiply the numerator and denominator of each fraction by the same number needed to make the denominator equal to 6:


(1)/(6),\;\;(1\cdot 2)/(3\cdot 2),\;\;(1\cdot 3)/(2\cdot 3),\;\;(2\cdot 2)/(3\cdot 2),\;...


(1)/(6),\;\;(2)/(6),\;\;(3)/(6),\;\;(4)/(6),\;...

Notice that the numerator of each term is the position of the term.

Therefore, the next two terms (a₅ and a₆) of the sequence are:


a_5=(5)/(6)


a_6=(6)/(6)=1

Therefore, the rule for the nth term is:


a_n=(n)/(6)

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