Advanced Math/Math - Monomials
Hi, now I am learning a new topic in Math called "Monomials". Although I already learned a bit of ranks and terms ["r" and "t", for example] but we have just started a new topic and I do not completely understand.
- What monomial represents the rule for the following sequence?
- 2, 8, 18, 32, 50, 72
- So I did the following calculations:
- So what I noticed was that the differences between each "difference" was increasing/decreasing [depending on the order that you look at it], by four.
- So again, I will repeat the question "What monomial represents the rule of that following sequence?"
Hi. Before discussing monomials a little bit, I'll cut to the chase. If you divide the sequence by 2 you get the new sequence
Snew = 1, 4, 9, 16, 25, 36
which can be recognized as a sequence of perfect squares, so that
Snew = 2n^2 for n = 1 to 6.
A monomial, as I assume you know, is defined as a term in a multi-variate polynomial and looks like
(x1^e1)(x2^e2) ... (xn^en)
where n is the number of variables and the sum of the exponents is d = e1 + e2 + ... en. The monomial above has 1 variable, n, and is of degree 2. The sequence is generated by increasing n (an integer).
I was mystified for a while because the sequence associated with a monomial is usually defined as the number of terms which have n variables and is of degree d for d = 0, 1, 2, ... An expression for this involves the binomial coefficient formula (and it doesn't fit this problem, i.e., can't get the given sequence by specifying any combination n and d).
I'm curious what the definitions of the various quantities in your question are. Also, what level are you (grade, year in college)?