om cou Lara creates a sequence of patterns using sticks . She adds the same number of sticks each time. What is the pattern number of the pattern that is made from exactly 82 sticks? square

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om cou Lara creates a sequence of patterns using sticks . She adds the same number of sticks each time. What is the pattern number of the pattern that is made from exactly 82 sticks? square

Answer 1

Solving the equation for \( n \), we get \( n = 41 \). So, the pattern that is made from exactly 82 sticks is the 41st pattern.

Answer 2

## Step 1: First, we need to determine the number of sticks used in each pattern. For pattern 1, there is 1 stick. For pattern 2, there are 3 sticks. For pattern 3, there are 5 sticks. ## Step 2: We can observe that the number of sticks used in each pattern forms an arithmetic sequence with a common difference of 2. ### The formula for the nth term of an arithmetic sequence is \( a_n = a_1 + (n - 1) \times d \), where \( a_n \) is the nth term, \( a_1 \) is the first term, \( n \) is the term number, and \( d \) is the common difference. ## Step 3: In this case, we know the nth term (82 sticks), the first term (1 stick), and the common difference (2). We can substitute these values into the formula and solve for \( n \). ### \( 82 = 1 + (n - 1) \times 2 \)

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om cou Lara creates a sequence of patterns using sticks . She adds the same number of sticks each time. What is the pattern number of the pattern that is made from exactly 82 sticks? square

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