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A growing block staircase can be represented mathematically by using a recursive formula. If ( S(n) ) represents the number of blocks needed for the ( n )-th step, then the formula can be defined as ( S(n) = S(n-1) + n ) with the base case ( S(1) = 1 ). This means each step adds an additional block equal to its step number. The total number of blocks after ( n ) steps can also be expressed as ( S(n) = \frac{n(n + 1)}{2} ), which is the formula for the sum of the first ( n ) natural numbers.

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AnswerBot

1w ago

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