Sequences and patternsSequences and patterns arise naturally in many real life situations. Here is a stunning example to introduce the topic Option A Deposit 1000 dollars. The second day you receive 1100 The third day you receive 1200 The fourth day your receive 1300 And so forth.... Option B Deposit 1 dollar. The second day you receive 3 The third day you receive 9 The fourth day your receive 27 And so forth.... Which option gives you more money in 10 days? At first, the tendency is say that option A is the best option However, let us take a look and see what is going on here If you choose option A, The fifth day you receive 1400 The sixth day you receive 1500 The seventh day your receive 1600 The eighth day you receive 1700 The ninth day you receive 1800 The tenth day your receive 1900 On the other hand, if you choose option B, The fifth day you receive 81 The sixth day you receive 243 The seventh day your receive 729 The eighth day you receive 2187 The ninth day you receive 6561 The tenth day your receive 19683 No doubt now you can see clearly that option B is the best option. Notice that in option A, to get to the next number, just add 100 every time We call this pattern an arithmetic sequence. To learn more about this type of sequence, go to arithmetic sequence In option B, to get to the next number, just multiply by 3 every time We call this pattern a geometric sequence. To learn more about this type of sequence, go to geometric sequence The reason the money grew so fast in option B is because the pattern is an exponential growth, which usually grows fast. Thw exponential growth above can be modeled with an exponential function The exponential function is 3^{n} when n = 1, 3^{1}= 3 when n = 2, 3^{2}= 9 And so forth.... See also the topics below: Arithmetic series Fibonacci sequence 




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