On the first day it was posted online, a music video got 1090 views. The number of views that the video got each day increased by 20% per day. How many total views did the video get over the course of the first 21 days, to the nearest whole number?


This problem involves a geometric series, where the number of views each day increases by a constant ratio of 20% (or 0.20). Let's break it down step-by-step.

1. **Initial Number of Views**:  
   The video gets 1090 views on the first day.  
   Let's denote this as \( a = 1090 \).

2. **Daily Increase Rate**:  
   The number of views increases by 20% each day.  
   This means the common ratio \( r = 1 + 0.20 = 1.20 \).

3. **Number of Days**:  
   We need to find the total views over the first 21 days, so \( n = 21 \).

4. **Geometric Series Formula**:  
   The sum of the first \( n \) terms of a geometric series is given by:
   \[
   S_n = a \frac{1 - r^n}{1 - r}
   \]
   Plugging in the values:
   \[
   S_{21} = 1090 \times \frac{1 - (1.20)^{21}}{1 - 1.20}
   \]

5. **Calculating the Sum**:
   Let's compute this sum to get the total views.

Let's perform the calculation now.The total number of views the video received over the course of the first 21 days is approximately **245,278**.

Would you like more details on this calculation or have any further questions?

Here are some related questions you might be interested in:
1. How would the total views change if the daily increase rate was 15% instead of 20%?
2. What would the total views be after 30 days with the same 20% increase rate?
3. How do you calculate the views on a specific day, say the 15th day?
4. If the views decreased by 10% per day after the 21st day, how would you calculate the total views up to day 30?
5. How does the formula for the sum of a geometric series change if the increase rate is negative?

**Tip:** For geometric series problems, identifying the initial term and the common ratio is key to setting up the correct formula.

On the first day it was posted online, a music video got 1090 views. The number of views that the video got each day increased by 20% per day. How many total views did the video get over the course of the first 21 days, to the nearest whole number?

Find out how to calculate the total views of a music video that starts with 1090 views and grows by 20% daily over 21 days using the geometric series formula. This problem covers exponential growth, algebra, and series summation, suitable for Grades 9-12.

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