Pearl Joyce Berana, Jomari Montalbo, Daryl Magpantay
Batangas State University, Main Campus I, Batangas City, Philippines
beranapearljoyce@yahoo.com, jomari.montalbo@yahoo.com.ph,
magpantaydaryl@gmail.com
Date Received: September 30, 2015; Date Revised: November 3, 2015
Asia Pacific Journal of Multidisciplinary Research
Vol. 3 No. 4, 76-81
November 2015 Part V
P-ISSN 2350-7756
E-ISSN 2350-8442
On Triangular and Trapezoidal Numbers 627 KB 3 downloads
Pearl Joyce Berana, Jomari Montalbo, Daryl Magpantay Batangas State University, Main...
The nth triangular number, denoted by T (n), is defined as the sum of the first consecutive positive integers. It can be represented in the form of a triangular grid of points. As a result, this study discusses the triangular numbers and its properties. To distinguish whether a positive integer N is a triangular number or not, it has to comply with 8N + 1 which is a perfect square; characteristics of odd and even triangular numbers; sum of two consecutive triangular numbers with same parity i.e., the formula for2 )4()4()14( ccTcT where c ≥ 1 and2 )24()24()14( ccTcT where c ≥ 0; and introduces the new figurative numbers through deriving the formula of triangular number, Trapezoidal Number- an integer of1)( nT , denoted by T* (n)and Diamond Number- an integer ofnnT )(2 , denoted by D (n).
Keywords: Triangular numbers, Odd and Even Triangular numbers, Parity of triangular numbers, Trapezoidal number, Diamond number