Ads
related to: arithmetic sequences worksheets free download printable
Search results
Results From The WOW.Com Content Network
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
Download as PDF; Printable version ... The number of free ... At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous ...
Salem–Spencer sets are also called 3-AP-free sequences or progression-free sets. They have also been called non-averaging sets, [ 1 ] [ 2 ] but this term has also been used to denote a set of integers none of which can be obtained as the average of any subset of the other numbers. [ 3 ]
The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg , from a description of Morris in Clifford Stoll 's book The Cuckoo's Egg .
Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. As a third equivalent characterization, it is an infinite sequence of the form 1 a , 1 a + d , 1 a + 2 d , 1 a + 3 d , ⋯ , {\displaystyle {\frac {1}{a}},\ {\frac {1}{a+d}},\ {\frac {1}{a+2d}},\ {\frac {1}{a+3d}},\cdots ,}
The notion of an arithmetic progression makes sense in arbitrary -modules, but the construction of a topology on them relies on closure under intersection. Instead, the correct generalization builds a topology out of ideals of a Dedekind domain . [ 16 ]