Question

The bell rings ; the first step you take is half the distance 'd' from your desk to the door. Each step you take is half the previous distance. How far have you traveled after your sixth step ?

Answer 1

The bell rings ; the first step you take is half the distance 'd' from your desk to the door. Each step you take is half the previous distance. How far have you traveled after your sixth step ? ​

we know that

step 1 -------> d/2

step 2 ------> d/4

step 3 ------> d/8

step 4 -----> d/16

step 5 -----> d/32

step 6 -----> d/64

In exponential notation

Let

y -----> the distance

x -----> number of step

so

y=d(1/2)^x

Verify

For x=1

y=d(1/2)^1=d/2

For x=2

y=d(1/2)^2=d/4

For x=6

y=d(1/2)^6=d/64

therefore

After the sixth step the total distance traveled is equal to

d/2+d/4+d/8+d/16+d/32+d/64

so

(d/64)(32+16+8+4+2+1)

(d/64)(63)

(63/64)d

or 0.98d