Discussion

Explanation:

Sum of odd terms of a GP with first term a and common ratio = r is
a + ar² + ar⁴ + ar⁶ + … + ar⁹⁸ = 1122 …(1)

Sum of even terms of a GP with first term a and common ratio = r is
ar + ar³ + ar⁵ + ar⁷ + … + ar⁹⁹ = 1683 …(2)

Dividing (2) by (1),
$\frac{ar+a{r}^3+a{r}^5+a{r}^7+\dots +a{r}^{99}}{a+a{r}^2+a{r}^4+a{r}^6+\dots +a{r}^{98}}$ = $\frac{1683}{1122}$

∴ $\frac{ar\left(1+r^2+r^4+a{r}^6+\dots +a{r}^{98}\right)}{a\left(1+r^2+r^4+r^6+\dots +a{r}^{98}\right)}$ = $\frac{3}{2}$

∴ r = $\frac{3}{2}$

Hence, option (c).

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