IM Alg2.1.11 Practice: Adding Up
Find the sum of the sequence:
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.
What fraction of the length of the hallway will Priya have covered after she starts and stops two times?
What fraction of the length of the hallway will Priya have covered after she starts and stops four times?
Will Priya ever reach the end of the hallway, repeatedly starting and stopping at half the remaining distance? Explain your thinking.
A geometric sequence h starts with 10, 5, . . .
Explain how you would calculate the value of the 100th term.
Here is a graph of sequence r.
Define recursively using function notation.
An unfolded piece of paper is 0.05 mm thick.
Define for the term.
What is a reasonable domain for the function ? Explain how you know.
A piece of paper is 0.05 mm thick.
Does make sense? Explain how you know.
An arithmetic sequence a starts 84, 77, . . .
Define recursively.
Define for the term.
Here is a pattern of growing rectangles:
Describe how the rectangle grows from Step 0 to Step 2.
Write an equation for sequence , so that is the number of squares in Step .
Is a geometric sequence, an arithmetic sequence, or neither? Explain how you know.