Discussion

Explanation:

Let the first term and the ratio of the Geometric Progression be a and r respectively.
∴ a + ar = 12
∴ a(1 + r) = 12 … (1)

Also, ar² + ar³ = 48
∴ ar2(1 + r) = 48 …(2)

Dividing (2) by (1),
$\frac{{\mathrm{ar}}^2\left(1+\mathrm{r}\right)}{\mathrm{a}\left(1+\mathrm{r}\right)}$ = $\frac{48}{12}$ = 4
∴ r² = 4
∴ r = ± √4 = ± 2

Since the terms of the Geometric Progression are alternately positive and negative, r = −2

∴ From (1), a(1 − 2) = 12
∴ a = −12

Hence, option (c).

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