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Mathematics - Lecture 20: Arithmetic and geometric sequences

Mathematics - Lecture 20 provides knowledge of arithmetic and geometric sequences. The main contents of the chapter consist of the following: Sequences, arithmetic sequences, geometric sequences. | Arithmetic and Geometric Sequences Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 20 Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 1 / 23 Outline 1 Sequences 2 Arithmetic Sequences 3 Geometric Sequences Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 2 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Examples: 1 2, 4, 6, 8, 10, 12, . . . 2 2, 3, 5, 7, 11, 13, . . . 3 20, −10, 5, − 5 , 5 , − 5 , . . . 2 4 8 4 4, 2, 8, 6, 12, 10, . . . Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / 23 Sequences Definition A sequence is an ordered set of numbers. The numbers in the sequence are called terms. Examples: 1 2, 4, 6, 8, 10, 12, . . . 2 2, 3, 5, 7, 11, 13, . . . 3 20, −10, 5, − 5 , 5 , − 5 , . . . 2 4 8 4 4, 2, 8, 6, 12, 10, . . . The last sequence is different from the first sequence though the same numbers appear in the sequences. Math 17 (UP-IMath) Arithmetic and Geometric Sequences Lec. 20 3 / .