Algebra

Math patterns example 1 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

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Let’s say I have tables where I can gather one person on each of the two short sides. So one person can sit here And one can sit here Imagine we are looking at the table from above. We can put one person on each of the two short sides. Then on the long sides, here, we can put two people each. Two people on the long side. At one table you can gather 1, 2, 3, 4, 5, 6 people. You can accommodate 6 people. Let’s think about what will happen, when we reach more tables to this one. Now imagine two tables Here we have a table that will touch this side of this table. And since the two tables touch, this will become one big table. No one can sit here anymore. Now how many people can sit? Let’s see. 1, 2, 3, 4, 5 can sit here. And on this identical table, will sit 6, 7, 8, 9. And then we can put one person here at last. So when we have 2 touch tables, we can gather a total of 10 people. Let’s continue like this and see what the logic is. We will put 3 tables here – 1, 2 and 3. As before, we can put one person at each end. These are two people. Then we have 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 – 14 people. What happened? If you look at the numbers, we went from 6 through 10 to 14. Looks like we’re adding 4 people each time when we add mass. Is there any logic in this? Let’s think about the first situation. Imagine that these are real people, I will make this man blue. If we bring this new table, table number 2, if it is table 1, this blue man has to move. Where can I move? Let’s just say he wants to to sit at the end of the table. So the blue man will sit at the new end of the table. Move here. So how many more people can sit on this one double table? I will draw the new people in purple. The new people are this man, this person, this man and this man. So we managed to accommodate 4 more people at the new table. We can think of this table there will be one usable end here. This usable end will be occupied by man, who sat at the end when the tables were one less. So the real extra seats are these two countries. That is, we add 4 seats every time we add a table. This is completely logical. Based on that, you might think without even drawing how many people will fit on 4, 5, 6 or more of these tables You can imagine that if we have 4 tables, we just need to add 4, 18 people will be received. If we have 5 tables, 22 people will gather, etc.

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