• anonymous
Find the first 5 terms of the sequence: a1 = 2, an = -3an-1
  • Stacey Warren - Expert
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  • jamiebookeater
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  • welshfella
  • anonymous
No its a1 = 2, an = -3an-1
  • anonymous
\(a_1=2\) 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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