Good day everyone! How are you today? I hope you are fine.
Hi, I am teacher Melanie M. Helzano of the Nabunturan National Comprehensive High School, your mathematics grade 10 teacher for this You may call me Ma'am Melanie. Before we start our lesson, please find your most comfortable place to sit on and prepare your module with your pen. I will give you time to prepare. Are you ready? 5, 4, 3, 2, 1, 5, 10, 15, 20, 15, 13, 11, 9, Ring a bell.
Anybody who can remember this succession of numbers with fixed pattern? Correct! It is called an arithmetic sequence.
Did you know that arithmetic sequence is not the only sequence that follows a pattern? Right! There are other sequences aside from arithmetic. And that will be our topic today. Consider the following fractions.
2 fourths, 2 eighths, 9 thirds, 7 forty-ninths, 8 cubed, over a raised to 4. We can simply express these as 2 fourths equals 1 half, 2 eighths equals 1 fourth, 9 thirds equals 3. 7 49's equals 1 over 7. a cube over a raised to 4 equals 1 over a. As you have observed, there is a comparison of two numbers by division. And that comparison is called ratio. The concept of ratio help us understand more to the next kind of sequence. Now let us proceed to our next activity.
For this activity, I am using a bond paper whose one side measures 8 inches. Since this is a square, all sides are equal. So we will get the area by squaring the length of one side.
Therefore, giving us an area of 64 square inches. So learners, perform the paper folding and record the results in a table. Let us start with the big square from a piece of paper.
Again, having an area of 64 square inches. Next, fold the four corners of the paper to the center of the square. Measure the length of one side. Find the area.
Repeat the process 3 more times and tally the results. 32, 16, 8, 4, 2, 1 is the sequence that applies the concept of ratio. That's it!
A common ratio is obtained by dividing any term with the preceding term. For example, second term divided by first term equals 16 divided by 32 equals one half. Third term divided by second term. term equals 8 divided by 16 equals 1 half fourth term divided by third term equals 4 divided by by 8 equals 1 half and so on.
Therefore, 1 half is the common ratio and the sequence 32, 16, 8, 4, 2, 1 and so on is called Geometric Sequence A geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding term by the same non-zero constant called the common ratio. If we have 2, 6, 18, 54, and so on, is this a geometric sequence? Yes? Why? Very good!
This is because it has a common ratio. Thank you. Can you give me the common ratio of the sequence? 3?
Correct! The common ratio is 3. Therefore, it is a geometric sequence. Let us have the activity to make sure you understand geometric sequence. Get your module.
And your pen. Let us answer the activity on missing in action. Number 1, 3, 12, 48. What's the next term? Number 2. What's the first term?
12, 36, 108 Number 3 3x squared What's the second term? 3x to the power of 6 3x to the power of 8 Number 4 1 third 1 9th, 1 over 27, what's the 4th term? Let us see if you've got the correct answers. Very good!
Perfect! It is because you are so attentive. Like arithmetic sequence, each term in a geometric sequence is related in one way or another to the next or the preceding term. Let's exercise more.
Can you identify which of the following is a geometric sequence? Letter A, 125, 25, 5, 1, and so on. Letter B, 50, 35, 20, 5, and so on. Letter C, 1 half, 3 fourths, 1, 5 fourths, and so on.
Letter D, 5, negative 10, 20, negative 40, and so on. Correct! Excellent!
Letter A. It is a geometric sequence and one-fifth is the common ratio. Letter B. Yes, arithmetic sequence and negative 15 is the common difference. Letter C. Very good, arithmetic sequence and one-fourth is the common difference.
Letter D. Very good, geometric sequence and negative 2 is the common ratio. Now, can you identify geometric sequences? How will you know if a sequence is geometric and not arithmetic?
Can you distinguish geometric sequence from an arithmetic sequence? Is geometric sequence important in your daily lives? How does it affect our way of life?
Geometric sequence is a sequence where each term after the first is obtained by multiplying the preceding term by the same non-zero constant called the common ratio. It is easy to distinguish geometric from arithmetic. Geometric sequences have a common ratio while arithmetic sequences do not. have a common difference. Did you know that UPLB students use geometric sequence in predicting the number of COVID-19 positive cases for the month of August?
And with a small margin of error. I bet you didn't. If you don't know, well then, now you know. And that's our lesson for today. But before we go, remember, wash your hands, socially distance, stay healthy, physically, mentally, stay home, stay safe.
We're all in this together. Till next time, always remember, dito sa TV Eskwela, sa pag-aaral, sama-sama. Bye-bye! Music