Priya is walking down a long hallway. She walks halfway and stops. Then, she walks half of the remaining distance and stops again. She continues to stop every time she goes half of the remaining distance.

1. What fraction of the length of the hallway will Priya have covered after she starts and stops 2 times?
2. What fraction of the length of the hallway will Priya have covered after she starts and stops 4 times?
3. Will Priya ever reach the end of the hallway, repeatedly starting and stopping at half the remaining distance? Explain your thinking.

A geometric sequence starts with 10, 5, . . . Explain how you would calculate the value of the 100th term.

An unfolded piece of paper is 0.05 mm thick.

An arithmetic sequence  starts 84, 77, . . .

1. Define recursively.

2. Define for the term.

Here is a pattern of growing rectangles:

Three rectangles on a square grid. The first rectangle is a 1 by 3 rectangle, positioned vertically. The second rectangle has 12 squares with width 2, height 6. The third rectangle has 27 squares with width 3, height 9.

1. Describe how the rectangle grows from Step 0 to Step 2.
2. Write an equation for sequence  so that is the number of squares in Step .
3. Is a geometric sequence, an arithmetic sequence, or neither? Explain how you know.