Last winter, I was watching the first snow of the year as it began. As I
was watching, I noticed an interesting pattern: The first minute, only
one snowflake fell. During each passing minute, the number of
snowflakes that fell was equal to the total on the ground plus one.
If this pattern continued for the whole snowstorm, how many
snowflakes fell during the 12th minute? During the 24th minute?
To get 100% on this assignment, you must write a variable
expression that represents how many snowflakes would fall during
the nth minute.
Using a geometric sequence, it is found that:
- 2048 flakes fell during the 12th minute.
- 8,388,608 flakes fell during the 24th minute.
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
In which is the first term.
On the first minute, one flake fell. On the second minute, two flakes fell. On the third minute, four flakes fell(3 + 1). On the fourth minute, eight flakes fell(1 + 2 + 4 + 1). Hence the first term and the common ratio of the sequence are given by:
And the amount of flakes that fell in the minute n is:
In the 12th minute, the amount is given by:
In the 24th minute, the amount is given by:
More can be learned about geometric sequences at https://brainacademy.pro/question/11847927