Geometric Series: Anna and Birger walks at the same constant speed.

[Firas]

Anna and Birger walks at the same constant speed. They start at thesame place, facing in the same direction. Birger walked in that directionthroughout the time. Anna, however, turned 90 degrees to the rightimmediately after her first step. Then she turned another 90 degrees tothe right immediately after taking two more steps, and yet another 90-degree turn to the right immediately after taking four more steps. Shewalked this way, doubling the number of steps every time she turns.When Anna was about to turn for the 17th time, both of them stopped.If the ratio of the distance each has walked to the distance betweenthem at the end is ?: ? (simplest form), then write down the first fourdigit of? + ??

I know the formula : ar^n-1 for finding a certain term.
I also know the formula for finding the sum of the geometric sequence formula.

So, I think I know how to solve for the distance each has walked :

1 2 4 8 16 ....

(1-2^17) / (1-2) = 131071

But can you give me a way to find the distance between them.

 

[Steven G]

Anna and Birger walks at the same constant speed. They start at thesame place, facing in the same direction. Birger walked in that directionthroughout the time. Anna, however, turned 90 degrees to the rightimmediately after her first step. Then she turned another 90 degrees tothe right immediately after taking two more steps, and yet another 90-degree turn to the right immediately after taking four more steps. Shewalked this way, doubling the number of steps every time she turns.When Anna was about to turn for the 17th time, both of them stopped.If the ratio of the distance each has walked to the distance betweenthem at the end is ?: ? (simplest form), then write down the first fourdigit of? + ??

I know the formula : ar^n-1 for finding a certain term.
I also know the formula for finding the sum of the geometric sequence formula.

So, I think I know how to solve for the distance each has walked :

1 2 4 8 16 ....

(1-2^17) / (1-2) = 131071

But can you give me a way to find the distance between them.

What have you tried to find the distance between them. Try drawing a diagram! Please show us your work so we know where you need help.

 

[Dr.Peterson]

Anna and Birger walks at the same constant speed. They start at the same place, facing in the same direction. Birger walked in that direction throughout the time. Anna, however, turned 90 degrees to the right immediately after her first step. Then she turned another 90 degrees to the right immediately after taking two more steps, and yet another 90-degree turn to the right immediately after taking four more steps. She walked this way, doubling the number of steps every time she turns.When Anna was about to turn for the 17th time, both of them stopped.If the ratio of the distance each has walked to the distance between them at the end is ?: ? (simplest form), then write down the first four digit of? + ??

I know the formula : ar^n-1 for finding a certain term.
I also know the formula for finding the sum of the geometric sequence formula.

So, I think I know how to solve for the distance each has walked :

1 2 4 8 16 ....

(1-2^17) / (1-2) = 131071

But can you give me a way to find the distance between them.

She is walking in a sort of spiral, right?

Suppose they started facing east. How far has she walked to the east? How far to the north? Write those first as series, then simplify.