If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 2 (Eureka Math/EngageNY)>Unit 3

Lesson 12: Topic E: Lesson 29: Geometric series

# Finite geometric series word problem: social media

Watch Sal solve an example of using a geometric series to answer a fun word problem. Created by Sal Khan.

## Want to join the conversation?

• Sorry, but can anyone explain to me how Sal arrived at 1.47? Is " 1 " used to represent a month?
• Let say 1st month user = 50; and we need to add 47% each month.
To get 2nd month we need to have add first month user + 47% from 50 or 50 + (50 * .47)
We know 50 * 1 = 50 and 50 * .47 = 23.5
Combined together to get 2nd month we get: 50 * 1 + 50 * .47 = 73.5
Then factoring: 50 * (1 + .47) = 73.5
Or 50 * (1.47) = 73.5
Conclusion, we can get 2nd month by 50 * 1.47
• I think there must be a difference in the use of the word "through" between US and Australian English. I understood "through month n" to mean "from the start of month n to the end of month n" but from the math I gather that it means "from the start of the year to the end of month n". Could someone please confirm or deny that this is how you use "through"?
• I understand what you are asking.
I believe that the issue is interpretation of an accidentally unclear problem more than linguistic barriers. I can now see it from both perspectives, but I agree that in this problem - "through" means how many users were added from the beginning of the year to the end of month n.
• Why not the first answer, 50(1.47^n)?
- I see, by “new” users, the question is looking for how many users were added that month, not total users. I misunderstood the question.
• For new users added each month though, couldn't you just do 50*1.47^n-50, aka final - initial?
• Where might I find more solved examples of finite geometric series word problems? I am having great difficulties solving and visualizing them, and the two videos here are clearly not enough for me.
• How did Sal get 50 x 1.47^n at the end? How does 50 x 1.47^n-1 + .47 = 50 x 1.47^n
• Well, you start the month with a certain number, then you add some during the month, and the last column is the total number at the end of each month.

50 times (1.47)^(n-1) times 0.47
So by the end of the nth month we have:
50 ∙ `(1.47)^(n-1)` + 50 ∙ `(1.47)^(n-1)` ∙ 0.47
To simplify, we can factor out a 50 to leave
50 [`(1.47)^(n-1)` + `(1.47)^(n-1)` ∙ 0.47]
now if we factor out the remaining common factor of `(1.47)^(n-1)`
we get
50 (`(1.47)^(n-1)`) [1 +∙ 0.47]
That 1 +0.47 is just another 1.47, so we now have
50 (`(1.47)^(n-1)`) (1.47)
50 `(1.47)^(n-1+1)`
50 `(1.47)^n`
• this video is different from the other problems and what did the third sentence mean by n is grater than or equal to 1 and n is smaller than or equal to 12?
• It's just saying that the expression will only be valid if n is some value from 1 to 12. The social media site only made a claim about one year, and there are 12 months in a year!
• Couldn't it be expressed also as ∑ where n=1 to 12 with 50,000(0.47)^(n-1) ?
• Not quite. It would be ∑ where n=1 to 12 of (0.47)(50)(1.47)^n-1.
If you look at the right answer choice, the constant coefficient is (0.47)(50) while only (1.47) is being taken to different powers.

I hope this helps you understand the answer in terms of a summation better!
• If suppose I get this question in an exam then how would I know it forms AP or GP by reading the problem?
I am sorry but I am unable to distinguish despite knowing that AP is what we get by add/subtract and GP by multiplication

• Think about what happens to the initial term, in this case the 50,000 social media users.

In February they will have increased by 47%, which would be an increase by 23,500 users to 73,500.

If this is an arithmetic sequence, then the users will increase by 23,500 every month, but 23,500 is not 47% of 73,500, so it can not be an arithmetic sequence.

Rather, the number of users would increase by 34,545 to 108,045.

If this is a geometric sequence, then we should see that the ratio between two consecutive terms is constant, and sure enough
108,045∕73,500 = 73,500∕50,000 = 1.47, which makes sense since we're dealing with a 47% increase every month.