Let t0 = a

Then

> t1 = t0 + 0.01*t0 = 1.01*t0

And

> t2 = 1.01*t1 = 1.01*1.01*t0

> t3 = 1.01*t2 = 1.01*1.01*1.01*t0

> …

> tn = (1.01)^n * t0

So a cotton shirt weighs about 5oz on average, which is 0.3125 pounds. Let’s say that the flag would take only 20% (i.e. 1 shirt makes 5 flags) of the shirt fabric to make one, which gives 0.0625 pounds.

In 1969 when Apollo 11 launched, there were 126 nations in the UN. Adding the 50 states gives a total amount of 176 flags on board the spacecraft.

176 flags times 0.0625 pounds per flag gives 11 pounds total. Kind of a negligible amount.