You are here:

Advanced Math/Math - Monomials

Advertisement


Question
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:
  - 72-50=22
  - 50-32=18
  - 32-18=14
  - 18-8=10
  - 8-2=6

- 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.

  - 22-18=4
  - 18-14=4
  - 14-10=4
  - 10-6=4

- So again, I will repeat the question "What monomial represents the rule of that following sequence?"

- Thanks

Answer
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)?

Randy

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography

©2016 About.com. All rights reserved.