Select the correct option that will fill in the blank and complete the series.1024, ?, 1600, 2000, 2500, 3125

Let's find the ratio between consecutive numbers at the end of the series:
$$\frac{3125}{2500}=\frac{5}{4}=1.25$$
$$\frac{2500}{2000}=\frac{5}{4}=1.25$$
$$\frac{2000}{1600}=\frac{5}{4}=1.25$$
The series follows a geometric progression where each term is multiplied by $\frac{5}{4}$ (or $1.25$) to get the next term.Let the missing term be $x$.
$$1024\times \frac{5}{4}=x$$
$$x=256\times 5=1280$$
Let's verify if $1280\times \frac{5}{4}=1600$:
$$1280\times \frac{5}{4}=320\times 5=1600$$
Thus, the missing number is 1280.