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### Course: Algebra 1 > Unit 9

Lesson 1: Introduction to arithmetic sequences- Sequences intro
- Intro to arithmetic sequences
- Intro to arithmetic sequences
- Extending arithmetic sequences
- Extend arithmetic sequences
- Using arithmetic sequences formulas
- Intro to arithmetic sequence formulas
- Worked example: using recursive formula for arithmetic sequence
- Use arithmetic sequence formulas

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# Extending arithmetic sequences

Sal extends the arithmetic sequences -8, -14, -20, -26,... and 2, -1, -4, -7, -10,... to find their next terms.

## Want to join the conversation?

- I always assume things I learn hear will help me on the exam. Then I got to the exam or compare notes to what the professor is teaching in the class and they are totally different. These examples are very simplified and lacking in depth. Why is this?(0 votes)
- They only teach you the basics and the formula, as for the harder problems, you just have to plug in the formula and think about it.(9 votes)

- Why do questions that look hard end of easy once when you know them?(8 votes)
- Because your brain has learned them! once you have learned them its actually easy, I think its because you know what symbols like ^ and letters in math mean. for example

K = 4

2^5*4(25 +3)+k12*1^99

2^5 means 2 to the fifth power, which is 32. 32*4(25 +3) means 32 times (4*28). 4*28 = 112, 32 * 112 = 3584. k12 means k times 12 which means 4 times 12, which is 48. 1^99 means 1 to the 99th power, which is 1, as 1*1 will always equal 1. meaning the final result of the problem is 3584 + 48 = 3632.(1 vote)

- Which grade that will learn this lesson?(5 votes)
- This is in the Algebra 1 section, so I'll say it's in 9th grade.(8 votes)

- what job will this be needed for?(4 votes)
- This helps make other math clearer in the future. That's what math is for. Without arithmetic you couldn't understand Algebra. Without understanding simplification of equations you couldn't easily understand simplification of inequalities. Etc. Etc.

Hope this helps!(7 votes)

- why is it the more u practice the easier it becomes over time?(4 votes)
- 'Cause practice makes perfect! It just gets the idea closer and closer to your mind until it's locked in there!😁(6 votes)

- For me it was the other way around.(6 votes)
- What website did he used for practices?(2 votes)
- It is KhanAcademy in its original format.(3 votes)

- Best way that I see, is to consider things in terms of moving on number line(2 votes)
- What is N in the formula??(1 vote)
- n is a placeholder for the term that you are interested in, it could be any term. If you ever see (n-1), that is the previous term to the one you are interested in. In general, n is an integer that is usually either >=1 or >1.(3 votes)

- When do you have to find the formula for the sequence to find the next few numbers to the sequence or is it superfluous to find the formula?(1 vote)
- When you only need to find the next few terms, you really can do without the formula, but if you are trying to find the 24th or 36th term, you do not want to write the whole sequence, you want to find an equation and plug the number in. So you have to decide when it becomes easier to find and use an equation as opposed to writing terms.(2 votes)

## Video transcript

- [Voiceover] We're told
the first four terms of an arithmetic sequence are given. So it goes from negative
eight to negative 14 to negative 20 to negative 26. What is the fifth term in the sequence? So we just need to
figure out the next term. Well, in arithmetic sequence, each successive term is
separated by the same amount. So when we go from negative
eight to negative 14, we went down by six and
then we go down by six again to go to negative 20 and
then we go down by six again to go to negative 26, and
so we're gonna go down by six again to get to negative 32. Negative 32. Let's do a couple more of these. The first five terms of
the sequence are given. What is the sixth term? Let's see, to go from two to negative one, you subtracted three. Two minus three is negative one. Negative one minus three is negative four. Negative four minus
three is negative seven. Negative seven minus three is negative 10. And so negative 10 minus
three is negative 13. So hopefully that gives
you the hang of things.