2, - 6,12, - 20,30 and - 42 constitute a sequence to find the general term formula | Math enthusiast | Mathematical art

2, - 6,12, - 20,30 and - 42 constitute a sequence to find the general term formula

Let's look at their absolute values first
bn=|an|
be
b2-b1=4
b3-b2=6
b4-b3=8
……
bn-b(n-1)=2n
Add
bn-b1=2*(2+3+…… +n)=2*(n+2)(n-1)/2=n^2+n-2
b1=2
bn=n^2+n
So an = (- 1) ^ (n + 1) * (n ^ 2 + n)

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