Generate a formaula for nth Octogonal number.

Question

Generate a formula for the nth Octagonal number by relating to one or more figurate numbers with fewer than seven sides(by relating to hexagonal, pentagonal, square, oblong or triangular numbers).

Answer 1

Step 1:

The figurative number of a triangle is .

The figurative number of a square is .

Rewrite the expression of square as .

The figurative number of a pentagon is .

The figurative number of a hexagon is .

Rewrite the expression of hexagon as .

The figurative number of a heptagon is .

Observe the sequence of triangle, square, pentagon, hexagon and all.

The coefficient of n is increasing by 1 and the constant is reduced by 1 number.

Hence, the figurative number of a octagon is .

Solution :

The figurative number of a octagon is .