The total amount of sugar Lana used in each batch is decreasing by three-fourths each time. To find the total amount of sugar she uses for the first 6 batches, we can use a geometric sequence.
The first term in the sequence is 500 grams of sugar, and the common ratio is three-fourths (or 3/4).
Thus, the expression to find the total amount of sugar used in the first 6 batches is:
500 + (500 * (3/4)) + (500 * (3/4)^2) + (500 * (3/4)^3) + (500 * (3/4)^4) + (500 * (3/4)^5)