Question

Consider a chessboard, which has a total of 64 squares. one grain of rice is placed on the 1st square, 2 grains on the 2nd square, 4 grains on the 3rd square, 8 grains on the 4th square, and so on. how many grains of rice will be placed on square number 18?

Answer 1

We can model with the following formula:
$u_1=1,u_2=2,u_3=2^2=4,u_4=2^3=8....u_n=2^{n-1}$
So, for n=18 we compute like this the number of grains:
$u_{18}=2^{17}=131072\text{ grains}$