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## Algebra 2 (Eureka Math/EngageNY)

### 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.

On the nth row, we start with 50 times (1.47)^(n-1)
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?
(1 vote)
• 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

(1 vote)
• 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.