Half of the people on a bus get off at each stop after the first, and no one gets on after the firsh stop. If only one person gets off at number 7, how many people got on at the first stop?

Let,

Number of people got on at the first stop = x

 After the first stop, people left on the bus = (1/2)*x 

At the second stop, (1/2)*x people get off, leaving (1/2)x(1/2) = (1/4)*x people on the bus.

At the third stop, (1/4)*x people get off, leaving (1/4)x(1/2) = (1/8)*x people on the bus.

This pattern continues until the seventh stop, where only one person gets off the bus.

So, at the seventh stop, there are (1/2)^6 * x = (1/64) * x people on the bus.

Since there's only one person left on the bus at the seventh stop, we can set up the equation:

(1/64) * x = 1

Now, let's solve for x:

x = 1 * 64 x = 64