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### Course: Class 10 (Old)>Unit 5

Lesson 1: Intro to arithmetic progressions

# Explicit formulas for arithmetic sequences

Sal finds explicit formulas of arithmetic sequences given the first few terms of those sequences. He also explores equivalent forms of such formulas.

## Want to join the conversation?

• I'm a little confused. So it states f(n)=12-7(n-1), so if n=4 we have
f(n)= 5(3) = 15 this is wrong tho.....
But if n=2 we get f(n)=12-7(2-1) =5 which is correct.
• Just use Order of Operations, and you will get the right answer for every term
So for n=4, first use the equation f(n) = 12 - 7(n - 1), plug in 4 for n. Then, in the parenthesis, you will have 4-1, which is 3. Then, multiply 7*3 = 21. Lastly, subtract 12 from 21, to get -9, which is the correct answer. When using arithmetic sequence formula. Always do the operation inside the parenthesis first, then multiply the result by the number outside the parenthesis( this is the common difference). Lastly take the product of that operation, and subtract/add (depends on the product!) to the first number ( which is the first term of the sequence. Do this, and because you are using order of operations, you will find the right term, no matter what sequence it is.
• who is the guy who makes all these videos?
• The "guy" is Salman "Sal" Khan, the founder of the site.
"Sal
Founder & CEO
Sal started Khan Academy in 2005 to help his cousins (and soon other people's cousins). In addition to setting the vision and direction for Khan Academy, he still makes a lot of videos (although he's not the only one anymore).
Sal holds three degrees from MIT and an MBA from Harvard."

Or here: https://en.wikipedia.org/wiki/Sal_Khan for a longer one.
• At about Sal shows the explicit formula, but in school I learned it the way shown below.
Is the formula I use and the formula in this video the same?
12, 5, -2, -9
a1=-7n+19
a1=-7(1)+19
a1=-7+19
a1=12

a2=-7n + 19
a2=-7(2)+19
a2=-14+19
a2=5

a3=-7n + 19
a3=-7(3)+19
a3=-21+19
a3=-2

a4=-7n + 19
a4=-7(4)+19
a4=-28+19
a4=-9
• Your function is ok. If you take Sal's function and simplify it, then you get your version. Sal's version is a little more common form because it can quickly be converted to recursive form.
Hope this helps.
• When I was a teen this stuff wasn't talked about at all in school; I got all the way through two college pre-calc classes without ever seeing anything to do with sequences. I wonder what caused it to be added in?
• Half of school is basically pointless. Most people will never need to know how to find the sixth term in an arithmetic sequence or how to define appropriate quantities for modeling. In my opinion, regular school should end at around 6th or 7th grade, and then ages 11–18 should be spent learning real-world problems (i.e., how to earn passive income, how to buy real estate, how to drive) and reviewing what they already learned in school. HOWEVER, I also believe that for those who want to pursue careers like physics, astronomy, math, or engineering (these are just a few), I would suggest they continue school and learn all that they can to be as successful as possible in their careers.
• But what if you have to find a sequence in between two other sequences? How would you solve it then? Is there another video a problem like that?
• Is f(n) = 12 - 7 (n - 1) same as f(n) = 12 - 3.5 (n - 2)?
Plz help
Thanks!
• You can determine this by trying some value of "n".
If n=1:
Your first equation creates: 12-7(1-1) = 12-0 = 12
Your second equation creates: 12-3.5(1-2) = 12+3.5 = 15.5
So, they aren't the same. They create different output values.
• Okay if I wanted to know the arithmetic sequence how do I go about solving for a new arithmetic sequence from a previous arithmetic sequence, how do I go about it, here is my example:
17, 22, 36, 37, 52, 24 ----to get----> = 14, 22, 52, 54, 59, 4
20, 21, 23, 38, 42, 6 -----to get---> = 22, 27, 35, 37, 45, 3
especially having to handle the general term of "n" as part of this problem. How would I go about finding a sequential solution to this problem?
• How to solve this problem : for a particular sequence the first term is 3 and the explicit formula is t sub n = -2tsub n -1 + 1, find the sixth term
• Probably a basic question, but is there a lesson or anything that explains why we don't distribute the -7 in f(n)=12-7(n-1)?

I'm assuming it's kind of just implied when dealing with functions, but I can't help but get the urge to distribute whenever I see a number to the left of things in parenthesis.
• As an explicit function you totally could, when learning about arithmetic sequences you normally won't just to be super clear it was an arithmetic sequence. But the point of turning it into an explicit function is that you ca treat it like a normal linear equation.

If you have them in the recursive form when you see it in a problem it will be obvious the n-1 and whatnot won't get numbers distributed because they will be subscripts (small numbers in the lower right) but it may be a little tricky if you type it out. Just be aware if it is in recusrive form or function form.

Let me know if that didn't help.
• So how do you Learn to multiply??