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# Using arithmetic sequences formulas

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

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• 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.
• why are there random numbers whyyy please explain what is happeninnng
• The second question can also be done as follows:
Given:
a1 = -7
ai = a(i-1) -2
=> common difference = d = -2
We know that:
an = a1 + (n-1)d
=> a5 = -7 + (4)-2 = -7 - 8 = -15
• 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.
• 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.
• This video confuses me. How can "4 + 3(i - 1)" possibly define an arithmetic sequence? It relies on multiplication, not addition, and therefore there is no common difference between terms.
(1 vote)
• Remember, multiplication is repetitive addition. As you go term to term, you are adding the same number every time.
3+3 is the same as 3*2
3+3+3+3+3 is the same as 3*5
The common difference is the 3 and the (i-1) tells you how many 3's are getting added together.