Question

A sequence of patterns is made from hexagons and triangles. The same number of hexagons and the same number of triangles are added each time. How many triangles are there in pattern number 60? ​

Answer 1

There are 122 triangles in pattern number 60.

Explanation:

Given:

U₁ = 4

U₂ = 6

U₃ = 8

U₄ = 10

We can see that U₁, U₂, U₃ & U₄ are making a pattern of arithmetic sequence, where the difference is:

U₂ = U₁ + d

6 = 4 + d

d = 2

`\boxed{U_n=U_1+(n-1)d}`

Therefore:

Uₙ = 4 + (n-1)(2)

= 4 + 2(n-1)

U₆₀ = 4 + 2(60-1)

= 122