Question

The total number of shaded triangles in the first 10
Sierpinski triangles is

Answer 1

Step-by-step explanation:

N=3^K-1 I really don't know how to explain it but that's the formula

The total number of shaded triangles in the first 10 Sierpinski triangles is  ⇒ 29,524.

Answer 2

The shaded triangle is an illustration of patterns

The total number of shaded triangles in the first 10 Sierpinski triangles is 55

From the question, we have:

Pattern = 1, Shaded triangle = 1

Pattern = 2, Shaded triangle = 3

Pattern = 3, Shaded triangle = 6

Pattern = 4, Shaded triangle = 10

So, the number of shaded triangle follows the rule:

$T_n = n + T_{n -1}$

When n = 10 i.e. when the pattern is 10, we have:

$T_{10} = 10 + T_9$

Calculate T9

$T_9 = 9 + T_8$

The sequence continues, as follows:

$T_8 = 8 + T_7$

$T_7 = 7 + T_6$

$T_6 = 6 + T_5$

$T_5 = 5 + T_4$

So, we have:

$T_5 = 5 + 10 = 15$

$T_6 = 6 + 15 = 21$

$T_7 = 7 + 21 = 28$

$T_8 = 8 + 28 = 36$

$T_9 = 9 + 36 = 45$

$T_{10} = 10 + 45 = 55$

Hence, the total number of shaded triangles in the first 10 Sierpinski triangles is 55

Read more about sequence and patterns at:

https://brainly.com/question/15590116