Question

Math

Posted 3 months ago

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Answer from Sia

Posted 3 months ago

Pattern Sequences

Pattern 1

In Triangle A, the sum of the numbers in the smaller triangles (8, 3, 18) is $8 + 3 + 18 = 29$. The number at the top vertex is $5$

Pattern 2

In Triangle B, the sum of the numbers in the smaller triangles (9, 4, 24) is $9 + 4 + 24 = 37$. The number at the top vertex is $4$

Pattern Rule

The sum of the numbers in the smaller triangles is equal to the top vertex number multiplied by a constant factor.

Answer

In Triangle C, the top vertex number is $9$. To find the missing number in the top center triangle, we use the pattern rule to determine the constant factor. For Triangle A, $29 = 5 \times k$ and for Triangle B, $37 = 4 \times k$. Solving for $k$ gives us $k = 29/5 = 5.8$ and $k = 37/4 = 9.25$. Since these factors are not consistent, we need to re-evaluate the pattern.
Upon closer inspection, we notice that the sum of the numbers in the smaller triangles is actually 7 more than the top vertex number multiplied by 4. For Triangle A, $29 = 5 \times 4 + 7$ and for Triangle B, $37 = 4 \times 4 + 7$. Applying this to Triangle C, we have $9 \times 4 + 7 = 36 + 7 = 43$. Therefore, the missing number in the top center triangle of Triangle C is $43 - (5 + 5) = 33$.

Key Concept

Pattern Recognition and Arithmetic Operations

Explanation

The key to solving the pattern is recognizing the relationship between the sum of the numbers in the smaller triangles and the top vertex number, then applying arithmetic operations to find the missing number.

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