Types of Numbers

Even numbers are 2, 4, 6, 8, 10, … … 2𝑛

Odd numbers are 1, 3, 5, 7, 9, … … (2𝑛−1)

Two consecutive integers are 𝑛 and 𝑛+1

Prove that the following statement is not true: The sum of two consecutive prime numbers is always even. 2 and 3 are prime 2 + 3 = 5 which is odd!

Triangular numbers are found by adding consecutive numbers.

The first ten Triangular numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55

First Triangular number is        0 + 1 =  (1 × 2)/2  = 1

Second Triangular number is   1 + 2 = (2 × 3)/2 = 3

Third Triangular number is      3 + 3 = (3 × 4)/2  = 6

Fourth Triangular number is   6 + 4 = (4 × 5)/2  = 10

Fifth Triangular number is      10 + 5 =  (5 × 6)/2 = 15

nth Triangular Number is  TN = 1 + 2 + 3 + . . . + (n – 1) + n   = n(n+1)/2