Math question please help

Question

1)    Zeno Jr. is standing 16 feet from the door. Each step he takes to the door covers half the distance left to the door.

a.   Predict how far Zeno Jr. will still be from the door after 4 steps.

Answer 1

First step 8ft, still 8ft from the door

Second step 4ft, still 4ft from the door

Third step 2ft, still 2ft from the door

Fourth step 1ft, still 1ft from the door

This is a geometric series

a_n=a₀(r)ⁿ

Where a₀ is the initial distance 16ft, r is the factor by which it is multiplied each time (1/2), n is the number or steps taken, and a_n is distance left to the door

a_n=16(1/2)ⁿ