To find the thirty-second shape of the pattern, we first need to understand the repeating sequence: "circle, diamond, sphere, circle, square." This sequence has 5 shapes in total.
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To find the thirty-second shape of the pattern, we divide 32 by the number of shapes in the repeating sequence, which is 5.
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So, we calculate 32 divided by 5:
\( 32 \div 5 = 6 \) with a remainder.
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To find the remainder, we multiply the whole number part of the division (which is 6) by the number of shapes (5):
\( 5 \times 6 = 30 \).
Then, we subtract this from 32:
\( 32 - 30 = 2 \).
Thus, the remainder is 2.
- Now, we look at the position of the remainder in the repeating pattern:
- 1 = circle
- 2 = diamond
- 3 = sphere
- 4 = circle
- 5 = square
Since the remainder is 2, the thirty-second shape corresponds to the second shape in our pattern, which is a diamond.
Putting it all together:
To find the thirty-second shape of the pattern, choose 32 by 5. The remainder is choose 2, making the thirty-second shape a choose diamond.