# Triangular and Stellar Numbers

Math I.B Internal Assessment: SL Type 1

Stellar Numbers

Raj Devraj

Math I.B Internal Assessment: SL Type 1

Stellar Numbers

6/26/2011

St. Dominics International School

Raj Devraj

## GENERAL STATEMENT: NTH TRIANGULAR NUMBERS IN TERMS OF N.

The differences between the sequences of terms:

According to Finite Differences if the 3rd difference of a pattern is 1, then the general term is a quadratic equation:
Thus to find the general term we must first find the value of ‘c’:

In order to find the values of ‘a’ and ‘b’ we must solve a quadratic using simultaneous equations, thus:

Substitute the value of ‘a’ of one equation:

To find the General statement that represents the nth triangular number in terms of ‘n’, we substitute the value of ‘y’ by Un and the value of ‘x’ by n, thus:

## NUMBER OF DOTS TO S6 STAGE

Thus, using finite difference:

The most obvious pattern is that the 1st row all numbers and odd and the second row all are even.

Also all these numbers are some multiples of 12 + ...