What is the value of X in the sequence 20, 10, 10, 15, 30, 75, X?

The correct option is 225.

To find the value of $X$ in the sequence 20, 10, 10, 15, 30, 75, $X$, we need to determine the mathematical relationship between consecutive terms. Let's analyze the ratio of each term to its preceding term:
First term to second term: $\frac{10}{20}=0.5$ (or multiplying by 0.5)
Second term to third term: $\frac{10}{10}=1$ (or multiplying by 1)
Third term to fourth term: $\frac{15}{10}=1.5$ (or multiplying by 1.5)
Fourth term to fifth term: $\frac{30}{15}=2$ (or multiplying by 2)
Fifth term to sixth term: $\frac{75}{30}=2.5$ (or multiplying by 2.5)

We can observe a clear pattern in the multipliers: they start at 0.5 and increase by 0.5 at each step (0.5, 1, 1.5, 2, 2.5, ...).
Following this pattern, the next multiplier to find $X$ must be:
$2.5+0.5=3$

Therefore, to find the value of $X$, we multiply the sixth term (75) by 3:
$X=75\times 3=225$