Spot an arithmetic progression, find its common difference, and write a formula for its nth term. Then use it to find any term, or to find which term has a given value.
3 lessons, about 1 h 15 min3 simulations10 problems5 practice questionsPython in every lesson
Created by StemPy LabAn arithmetic progression is a list of numbers in which each term after the first is found by adding the same number to the term before it. That fixed number is the common difference d. It can be positive, negative or zero. To check a list, find every difference: they must all be equal.
The nth term of an AP with first term a and common difference d is a + (n − 1)d. Use it to find any term, to find which term has a given value, and to test whether a number is a term at all. Counting from the end of a finite AP, the nth term is l − (n − 1)d, where l is the last term.
When two terms of an AP are given, subtract them to find d, then find a. Three numbers in an AP are best written as a − d, a and a + d. Word problems become APs when an amount changes by the same step: fares, rows of seats, savings, salaries. Counting the numbers of a kind is also an AP problem.
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