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

## 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 is the nth term, is the first term, is the term number, and 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 .### \( 82 = 1 + (n - 1) \times 2 \)