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# Using arithmetic sequences formulas

Sal finds terms of arithmetic sequences using their explicit and recursive formulas.

## Want to join the conversation?

• To the people of Khan academy,
I get the concept of what they are asking you to determine here but I seriously don't get how to do it I have been stuck on this one subject for almost three months and I have gotten so many answers right and then comes my last questions before I am done with the subject and somehow I get it wrong I don't know if its the way I am doing the work right or if I have just been doing it all wrong and getting the answers right out of luck. Three months is a little long to be working on this exact thing because I have other things to do and my coach has assigned me this exact thing a couple of months ago so I can't just delete it completly from my assignments because she would know and then I would have to do it again! I am hoping that someone could please explain exactly how to do this arthemetic sequence stuff because its so confusing and drives me crazy!
-Thanks so much
🌟Starfire🌟 (The pop culture geek) 😎
• Well, it's too late for me to reply, but you should not look at it like that (frustrating). Breath, watch the video, listen in class, and most importantly, forget what you have learned and just relearn it because that's what you're probably doing wrong. It means nothing if you are practicing it, but doing it wrong, you can practice it for days, weeks months, but if you're doing it wrong, you'll never understand it.
- Me giving this answer because I don't know how to help you exactly, especially when 4 years have passed and your offline.
• The video sort of makes sense, but when I try the problems I get wildly wrong answers. How does one make sense of this.
• It is hard to say what is going wrong without some specific example(s). So if you can give a problem and how you are solving it and getting a wildly wrong answer, people can analyze this and help explain where to go from there.
• Is there a short cut to this? Let's say we had the same equations, but instead of looking for the 5th term, we were to look for the 16th term? It would take a really long time to get there, and this method is pretty slow.
• Yes... if you keep working thru the lessons on sequences, you will see techniques for calculating specific higher terms in the sequence.
• If you're given two successive terms, say 13 and 18, how do you find the 50th term? Can I make an equation like is given in the first problem?
• There isn't a way to find the 50th term if you are only given two terms. You need at least 3 terms to be able to know what the pattern is.

In another answer, they say that you can just add 5 to the previous term to find the next term. However, it's just as valid to say you can multiply by 18/13 to get the next term. Or you can say you add 5*(the placement of the number) to get the next number (which would lead to 13, 18, 28, 43). While "adding 5 to the previous number" is probably the pattern, it doesn't have to be, and you shouldn't assume that it is on a test... or in real life.
• why are there random numbers whyyy please explain what is happeninnng
• I understand the Recursive Formula, but is there a faster way do do it??
• The faster way is to convert the recursive formula into an explicit formula which lets you get any term with minimal effort.
• I got the problem a(n)=-6-4(n-1) Find the fourth term in sequence.
I got (-)30, but it said the answer is (-)18.
Heres my reasoning:
(4-1)=3
-6-4 =-10
-10*3=-30

• You didn’t follow the order of operations. So what you did was (-6-4)*3, but what you need to do is -6-4*3. So you multiply 4*3 first to get 12, then take -6-12=-18. If you forgot the order of operations, remember PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
• Where does the -1 come from? We are adding in order to be in a sequence.
• The -1 comes from trying to get the number before. i.e in the recursive formula, you are adding/subtracting x amount from the term before. So, to get to term 20, you add something to term 19. This is why n-1 is needed. This is also why you need to know the first term in the sequence for the recursive formula.