Find the 1st four hexagonal numbers and the formula
The difference of two squares a2 - b 2 can be found in
16sq2 – 13sq2 = 3(16 + 13) = 3 . 29 = 87
To find the 1st four hexagonal numbers and the formula, let's start by understanding what a hexagonal number is.
A hexagonal number is a figurate number that represents a hexagon shape. It is given by the formula:
H(n) = n(2n - 1)
where 'n' represents the nth hexagonal number.
To find the 1st four hexagonal numbers, we can substitute different values of 'n' into the formula and calculate the result.
Let's calculate the first four hexagonal numbers:
For n = 1:
H(1) = 1(2 * 1 - 1) = 1(2 - 1) = 1 * 1 = 1
For n = 2:
H(2) = 2(2 * 2 - 1) = 2(4 - 1) = 2 * 3 = 6
For n = 3:
H(3) = 3(2 * 3 - 1) = 3(6 - 1) = 3 * 5 = 15
For n = 4:
H(4) = 4(2 * 4 - 1) = 4(8 - 1) = 4 * 7 = 28
So, the first four hexagonal numbers are 1, 6, 15, and 28.
Now you have the formula to calculate any hexagonal number using the value of 'n'. Just substitute the value of 'n' into the formula H(n) = n(2n - 1), and you'll get the corresponding hexagonal number.