For the pattern below, the total number of boxes used in Figure $n$ can be described by a arithmetic sequence. Write a recursive formula to find the number of boxes in Figure $n$.
Agure 1
figure 2
Figare 3

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Answer

$\boxed{T(n) = \frac{n(n + 1)}{2}}$

Steps

Step 1 ：The pattern is increasing by one box in each row, starting from the top. The total number of boxes in each figure can be calculated as the sum of the first n integers, where n is the number of rows in the figure.

Step 2 ：Using the formula for the sum of the first n integers, we get the recursive formula: $T(n) = \frac{n(n + 1)}{2}$

Step 3 ：$\boxed{T(n) = \frac{n(n + 1)}{2}}$

For the pattern below, the total number of boxes used in Figure $n$ can be described by a arithmetic sequence. Write a recursive formula to find the number of boxes in Figure $n$.Agure 1figure 2Figare 3

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For the pattern below, the total number of boxes used in Figure $n$ can be described by a arithmetic sequence. Write a recursive formula to find the number of boxes in Figure $n$.
Agure 1
figure 2
Figare 3