posted by Claudia on .
what are the similarities and differences between an arithmetic sequence and a linear equation?
ok i know that arithmetic sequence is a sequence of real numbers for which each term is the previous term plus a constant (called the common difference). For example, starting with 1 and using a common difference of 4 we get the finite arithmetic sequence: 1, 5, 9, 13, 17, 21; and also the inifinite sequence
1, 5, 9, 13, 17, 21, 25, 29, . . ., 4n+1, . . .
a linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one, two, three or more variables.
well the similarity would be that they both have a constant.
so how can i explain the difference?
would you give me an example so i can understand?
One difference is that a linear equation can have any values, the sequence only specific values.