Question

use the sequence and inductive reasoning to make a conjecture.
#9: is the 16th figure black or white?
#10: is the 19th figure black or white?
#11: what is the shape of the 10th figure?

Explanation:

Step1: Identify the color - pattern

The color pattern repeats every 3 figures: white, black, white.

Step2: Find the remainder for the 16th figure

$16\div3 = 5\cdots\cdots1$. The remainder 1 means the color is the same as the first in the 3 - figure pattern, which is white.

Step3: Find the remainder for the 19th figure

$19\div3=6\cdots\cdots1$. The remainder 1 means the color is the same as the first in the 3 - figure pattern, which is white.

Step4: Identify the shape - pattern

The shape pattern repeats every 3 figures: circle, square, hexagon.

Step5: Find the remainder for the 10th figure

$10\div3 = 3\cdots\cdots1$. The remainder 1 means the shape is the same as the first in the 3 - figure pattern, which is a circle.

Answer:

#9: White
#10: White
#11: Circle