Lesson 2.1 | Arithmetic Sequence

[00:00:00]Good morning, good afternoon and good evening students. It's your second week of this semester and now we will be proceeding on the lesson two of mathematics in the modern world revolving in arithmetic sequence in series. Um we will be first discussing about arithmetic sequence before we proceed on arithmetic series. Ready?

[00:00:22]Now flashed on your screen are the objectives that we wish to achieve by the end of this lesson. First, you should be able to determine the nth term of a number sequence. And second, generate a pattern to form a number sequence of your own.

[00:00:39]But before we proceed on arithmetic sequence, let's have a quick review of what we discussed in lesson one, which is the Fibonacci sequence or the Fibonacci numbers.

[00:00:50]Determine the missing values in the Fibonacci sequence below. Mainly the Fibonacci term 9 and the Fibonacci term 10. Take your time students.

[00:01:03]Now if you got 34 and 55 then very good again.

[00:01:11]Now students how are you able to solve for the missing terms in the Fibonacci sequence? Some of you might say the formula helped you in solving Fibonacci sequence while some of you might say you simply added the two preceding ones because again there's a pattern. I want you to hold on to that answer as we will be needing that all throughout our discussion today regarding arithmetic sequence. To formally begin our discussion, let's have some definition of terms. Starting with the word sequence. When we say sequence, it is a list of numbers that are organized in an ordered manner wherein each are referred to as term. That's why Fibonacci numbers are also called Fibonacci sequence because they involve a list of numbers that are organized in an ordered manner.

[00:02:03]On the other hand, when we say arithmetic, that is the branch or side of mathematics that involves numbers and the basic operations. Now as we know the Fibonacci sequence has this formula but then again the Fibonacci sequence is not the only sequence that is existing.

[00:02:21]That's why you might be wondering an formula for other arithmetic sequence.

[00:02:27]Now flashed on your screen is the basic or the general formula for arithmetic sequence wherein a subn is equal to a sub 1 + the quantity n minus one ultiplied to d where c a subn is our missing term. a sub1 is our first term in the sequence and the number of the term we want to find is represented by the letter n and letter d is our common difference. Let us put this formula into the test with this example.

[00:03:00]Look at the numbers. Let us first have our letter N or the the term that we are looking for. So based on our example, we are solving for the fifth term or the term number five. Therefore letter N I five. Now let us find a sub 1. A sub 1 is our first term and our first term is 6. Now look at the numbers 6 11 16 and 21.

[00:03:41]6k 11 aut 16 and 16k 21.

[00:03:48]Very good. Again our common difference is a five. Since we were able to substitute now the values that we have on our given formula, we can now proceed on solving for the value of a sub5 or the fifth term of our sequence. Now let us use PEMDAS in doing so. Beginning with letter P which means parentheses.

[00:04:12]Let us first solve for those numbers within the parentheses which is 5 - 1 which will give us four. Now next independence is E. We don't have that.

[00:04:24]Let's have M which is multiplication.

[00:04:28]So 4 * 5 that would be 20. Now after multiplication our D is division. We don't have that as well. So let's proceed with addition. 20 + 6 is equal to very good 26. Now our fifth term or the e of five or of our sequence is equal to 26.

[00:04:51]Now let's have another set of examples.

[00:04:55]Again we are solving we are still solving for a sub5 or the fifth term of our sequence. So our n is still five but this time our a sub one or the first term of our sequence is no longer um six now it's 56.

[00:05:15]Now look at our numbers. We have 56 48 40 and 32. Earlier I told you number sequence our common difference or the letter B letter D rather must be a positive number but this time.

[00:05:33]Therefore common difference is now a negative number 56 48 48 K 40 at 40 K 32.

[00:05:46]Very good aot I 8. But again our common difference is now a negative number.

[00:05:52]That's why now our common difference is -8. Again let us use PEMDAS or apply PEMDAS in solving for the fifth term of our sequence or the a sub5. Starting with the numbers in the parenthesis we have 5 minus one which is 4. Proceeding with multiplication. Now when we're multiplying two numbers with two different signs the sum the product rather will always be negative. So 4 * -8 that is -32.

[00:06:23]Now let us proceed with addition. 56 + -32. Now when you are adding numbers with two different signs it becomes subtraction. So subtract 56 and 32. Now ano signing difference nila.

[00:06:41]number difference with our equation 56.

[00:06:48]Therefore 56 and 32 the difference is 24 and since positive or mala positive number positive you difference. Therefore see a sub5 or the fifth term of our sequence is positive 24.

[00:07:07]Great job students for making this part.

[00:07:10]And now I think you're ready for our activity for this lesson.

[00:07:15]Your activity is to create your own arithmetic sequence by choosing a common difference. Again common difference or s letter D or number sequence manipulate your first term fix at two. So your formula below you use that to complete the five terms of your own arithmetic sequence. Again first terms first term fix or letter D.

[00:08:01]First term number two terms and that is basically it for the first part of our lesson two mainly the arithmetic sequence. The arithmetic series will be discussed in the second part of your lesson two.