Uni algebra, anyone help?

Let the original area = (A0).

After the 1st. 5-year period, lost area = (A0)/3.

So remaining area, (A1) = (A0) - (A0)/3 = (2/3).(A0).

After the 2nd. 5-year period, lost area = (A1)/3 = (1/3).(2/3).(A0)

So remaining area, (A2) = (A1) - (1/3).(2/3).(A0) = (2/3).(A0) - (1/3).(2/3).(A0) = (2/3)².(A0)

After the 3rd. 5-year period, lost area = (A2)/3 = (1/3).(2/3)².(A0).

So remaining area, (A3) = (A2) - (1/3).(2/3)².(A0) = (2/3)².(A0) - (1/3).(2/3)².(A0) = (2/3)^3.(A0)

Hence, after the nth. 5-year period,

lost area = (1/3).(2/3)^(n - 1).(A0).

For a time-period of 25 years, 25 years = 5 X 5-year periods.

Hence, for 25 years, n = 5.

Therefore, after 25 years, the lost area = (1/3).(2/3)^4.(A0) = 0.889.(A0)

So the fractional loss of original area = 0.889(A0) ÷ (A0) = 0.889 = 88.9%.

Skywave.

(2/3) of the original area remains after each 5-year period. In 25 years, there are 5 such periods. The amount lost is

.. 1 - (2/3)^5 = 0.868313 ≈ 86.8%