Question

While studying the properties of polygons, a mathematician comes across the following series. Find the next digit in the series.

• A. 12
• B. 13
• C. 14
• D. 15

Answer 1

The correct option is C 14

The numbers can be related to the number of diagonals in polygons.


Finding the relationship between the number of sides (n) of a polygon and the number of its diagonals (d), we get:

$d=\frac{n(n–3)}{2}$

Calculating the number of diagonals for a heptagon (7 sides), we get:

$d=\frac{7(7–3)}{2}=\frac{7\times 4}{2}=7\times 2=14$

Hence, the series can be completed as: 0, 2, 5, 9, 14