Sequences given by a formula or a rule, series and sigma notation, then arithmetic progressions in depth: the nth term, the sum, properties, and the arithmetic mean.
3 lessons, about 1 h 15 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabA sequence is a list of numbers in a definite order: a first term, a second term, and so on. It is a function whose inputs are the positions . The terms can come from a formula for or from a rule that builds each term from the ones before. Adding the terms gives a series, written with sigma notation. The partial sum adds the first terms, and .
An arithmetic progression (AP) adds the same number at every step. Its th term is , and the sum of its first terms is . Adding a number to every term, or multiplying every term by one, gives another AP. Terms the same distance from the two ends add up to . Three numbers in an AP are best taken as , , .
The arithmetic mean of two numbers and is , and , , form an AP. Three numbers , , are in an AP exactly when . To insert arithmetic means between and , split the gap into equal steps: . The means then add up to times the mean of and .
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