Alternating arithmetic‑geometric series

Find the sum of the first $2 p$ terms of the series $a + \frac{1}{3}, 3 a - \frac{1}{6}, 5 a + \frac{1}{12}, \dots$ .

~6 minAnswer checked instantlyArithmetic progressionGeometric progression

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.b, No. 14

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