Answer :
Answer:
The correct answers are Blue: [tex]\frac{1}{16}[/tex] square units ; Green: [tex]\frac{1}{64}[/tex] square units; and Yes the sum converges.
Step-by-step explanation:
Area of the largest triangle is 1 square unit.
The area of the triangle which are colored and follow a geometric sequence with the common ratio being [tex]\frac{1}{4}[/tex].
Area of the not shaded triangle is given by 1 square unit.
Area of the orange triangle is given by 1 × [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{4}[/tex] square units.
Area of the blue triangle is given by [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{16}[/tex] square units.
Area of the green triangle is given by [tex]\frac{1}{16}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex] square units.
If the pattern continues definitely then it becomes an infinite geometric progression series with common ratio [tex]\frac{1}{4}[/tex]. And thus the sum of area coverges as the ratio lies between -1 and 1.
Answer:
Blue: 1/16 square units.
Green: 1/64 square units.
If the pattern continues indefinitely, does the sum of the areas converge? Yes.
If the pattern continues indefinitely, the sum of the area is 1/3 square units.
Step-by-step explanation:
I got it all right.