Question 696834
A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equation. I know the answer because I used the calculator but I still want to know how to find the answer using a formula or equation.
----
Look at the pattern:
#1 term: 4096
---
#2 term: 4096(1/2) = 2048
---
#3 term: 4096(1/2)^2 = 1024
----
....
....
----
nth term: 4096(1/2)^(n-1)
------
You want to find "n" when you are told the term is 4
----
Solve: 4096(1/2)^(n-1) = 4
-------
Note: 4096 = 2*2*2*2*2...*2*2*2 = 2^12
----
So: (2^(12))(1/2)^(n-2) = 4
----
Then: (2^12))(2)^(2-n) = 4
---
2^(14-n) = 2^2
---
14-n = 2
---
n = 12
----
4 is the 12th term of the sequence.
================
Cheers,
Stan H.