In the seventh week, the lotus leaf area is exactly 1/4 of the pond area.

Let the area of the lotus leaf begin with x, the weekend of 1 is 2x, the weekend of 2*2x is 2 * 2x, and the weekend of 3 is 2*2*2x, and so on, which can be obtained by mathematical induction. The area of the lotus leaf in the nth week is 2 n * x, and then the area of the whole pond is 1, so there is

( 1/4)*2^9*x= 1/4

2^7*x= 1/4

That is, in the seventh week, it was 1/4.