Find a formula for the general term ⍺n of the sequence, assuming that the pattern of the first few terms continues.{-7, 14/3, -28/9, 56/27, -112/81, ...}

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Shea Pace · Accepted Answer

In the indicated order, we note thatBeginning with the first term, which is negative, the second term is positive, the third term is once more negative, and so on. We can therefore write it as (−1)n.Numertors in sequence are {7,14,28,56,112,…….} and as it is a geometric sequence with first term as 7 and common ratio 2. Therefore nth term is 7×2n−1.Denominators in sequence are {1,3,9,27,81,……..} again a geometric sequence with first term as 1 and common ratio 3. Then nth term is 1×3n−1=3n−1.Hence nth term αn=(−1)n7×2n−13n−1=−7⋅(−2)n−13n−1=−7(−23)n−1

Find a formula for the general term ⍺n of the sequence, assuming that the pattern of the first few terms continues. {-7, 14/3, -28/9, 56/27, -112/81, ...}

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