Question

Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} – T_n = 21, then n is equal to ______.

Options

• 5

• 7

• 6

• 4

Answer 1

Let T_n denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If T_{n + 1} – T_n = 21, then n is equal to 7.

Explanation:

According to the question,

^{n + 1}C₃ – ⁿC₃ = 21

`\implies` ⁿC₂ + ⁿC₃ – ⁿC₃ = 21

`\implies` ⁿC₂ = 21 = `(21 xx 2)/2` = `(7 xx 6)/2` = ⁷C₂

∴ n = 7