Alternate recurring series

Find the $n^{e x t t h}$ term and the sum to $n$ terms of the series $-\frac{3}{2} + 2 + 0 + 8 +
otdots$.

~15 minAnswer checked instantlyrecurring seriessum to n terms

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXIV. Recurring Series, Examples XXIV, No. 10

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).