Find the first 5 terms of the sequence: a1 = 2, an = -3an-1

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Find the first 5 terms of the sequence: a1 = 2, an = -3an-1

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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No its a1 = 2, an = -3an-1
\(a_1=2\) and \(a_n=-3a_{n-1}\), more likely. You know the first term (\(n=1\)), so you can find the second term (\(n=2\)). \[a_2=-3a_1=-3(2)=-6\] Because you know the second term, you can easily find the third (\(n=3\)): \[a_3=-3a_2=-3(-6)=18\] See the pattern? In general, you can find a closed form for the \(n\)th term. (A variety of methods exists, but basic pattern recognition is easy enough for this recurrence relation.) Each successive term is being multiplied by \(-3\). In fact, \[a_1=2=(-3)^0(2)\\ a_2=-6=(-3)^1(2)\\ a_3=18=(-3)^2(2)\] Judging by this, it looks like the \(n\)th term is given by \(a_n=2(-3)^n\). What do you get for \(n=5\)?

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