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## Class 10 (Old)

### 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.
• 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?
• 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
• 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.
• I'm having problems with this question, could anyone help me? Write the explicit formula for the arithmetic sequence.

2, -2, -6, -10, -14, ...
• So, the common difference is -4 and the first sequence is 2. Therefore, the explicit formula would be an = 2 - 4(n-1).
Hope this helps! If you have any questions or need help, please ask! :)
• How do you translate between recursive and explicit rules for arithmetic sequences?
• Find the first term a_1 and the common difference d. Then you can get the other formula quite easily.
Ex.) Find the recursive formula if the explicit formula is a_n = 5n - 3.
Let's find a_1 and d.
a_1 = 5 * 1 - 3 = 2
d = a_(n + 1) - a_n = 5(n + 1) - 3 - 5n + 3 = 5
Recursive formula:
a_1 = 2
a_n = a_(n - 1) + 5, where n = 2, 3, 4,...
(1 vote)
• I dont understand what did he mean
• At Sal is calculating the value for term 2 according to the second formula. The way he does this is buy slotting 2 into the function.

For example, the formula is f(n)=-150+50n. All we have to do here to find the value of the desired term is to slot the number we want to find into this function. If we want to find the value of the 2nd term the formula will become f(2)=-150+50*2. Now all we need to do is calculate that as per the operations. It becomes f(2)=-150+100 because 50 multiplied by 2 is 100. Then it becomes f(2)=-50 because -150 subtracted from 100 is -50.

No more working out is required, we have now found the value of term 2. If we want to find a different value we just slop another term into the original formula and perform the calculations.