Earlier, we learned that the  term of a geometric sequence with an initial value of and a common ratio of is .

For a Koch Snowflake, it turns out that we can find the number of triangles added on at each iteration by making and . The sum of the first terms in this geometric sequence tell us how many triangles total make up the th iteration of the snowflake

More generally, the sum of the first terms of any geometric sequence can be expressed as

or

1. What would happen if we multiplied each side of this equation by ?
   (Hint: .)

2. Rewrite the new equation in the form of .
3. Use this new formula to calculate how many triangles after the original are in the first 5, 10, and 15 iterations of the Koch Snowflake.

A music video is posted online and after a week it has 400,000 total views. The next day, the video has 13,000 new views, and each day following, the number of new views decreases by 12%.

1. How many people watched the video on the second, third, and fourth days after the decrease started?
2. How many total views will the video have after 28 days (21 days after the daily views started to decline)?