urp:algebra

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urp:algebra [2021-12-19] nerf_herder [Functions] |
urp:algebra [2022-02-01] (current) nerf_herder [Arithmetic Sequences] |
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https://courses.lumenlearning.com/suny-osalgebratrig/chapter/parametric-equations/ | https://courses.lumenlearning.com/suny-osalgebratrig/chapter/parametric-equations/ | ||

- | ==== Arithmetic Sequences ==== | + | ==== Arithmetic/Geometric Sequences ==== |

+ | | ||

+ | **Arithmetic sequence** has a constant difference between the terms, such as 1, 3, 5, 7, 9... | ||

Basic form to find term n: a(n) = a(1) + d(n-1), where d = step size (difference between terms), a(1) is the first term | Basic form to find term n: a(n) = a(1) + d(n-1), where d = step size (difference between terms), a(1) is the first term | ||

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If don't know last term, just substitute a(n): | If don't know last term, just substitute a(n): | ||

S = n/2 (2a + (n − 1) d) | S = n/2 (2a + (n − 1) d) | ||

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+ | **Geometric sequence** terms are found by multiplying the previous term by a constant, such as 2, 4, 8, 16 ... | ||

+ | |||

+ | a(n) = arⁿ⁻¹ | ||

+ | |||

+ | Other sequences exist: | ||

+ | * squares: a(n) = n², cubes, etc. | ||

+ | * triangular numbers: a(n) = n(n+1)/2 (number of dots in a triangle of n rows) | ||

+ | * fibonacci sequence: a(n) = a(n-1) + a(n-2) | ||

Convergence of a power sequence: http://math.bu.edu/people/prakashb/Teaching/32LS10/Lectures/11-2.pdf | Convergence of a power sequence: http://math.bu.edu/people/prakashb/Teaching/32LS10/Lectures/11-2.pdf |

urp/algebra.txt · Last modified: 2022-02-01 by nerf_herder