We encounter sequences at the very beginning of our mathematical experience. The list of even numbers 2, 4, 6, 8, 10, … and the list of odd numbers 1, 3, 5, 7, 9, … are examples. We can predict what the 20th term of each sequence will be just by using common sense. Another sequence of great historical interest is the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … in which each term is the sum of the two preceding terms. Sequences arise in many areas of mathematics: finance, radioactive decay and function approximation to name a few.
https://www.youtube.com/watch?v=aXbT37IlyZQ
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Number sequences and patternsArithmetic and geometric sequences (intro)Arithmetic and geometric sequencesSigma notation and recurrence relationsArithmetic and geometric series (with applications)More on finite and infinite geometric seriesReview