Consider the trapezoidal numbers 1 + 1 1 + 2 + 2 + 2 + 1, 1 + 2 + 3 + 3 + 3 + 2

Question

Consider the trapezoidal numbers 1 + 1 1 + 2 + 2 + 2 + 1, 1 + 2 + 3 + 3 + 3 + 2 + 1... The nth trapezoidal number is 1 + 2 where alpha is a positive integer complete parts (a)through (c) below. Notice that 1 + 1 + 1 = 1 times 3, 1 + 2 + 2 + 2 + 1 = 2 times 4, and1 + 2 + 3 + 3 + 3 + 2 + 1 = 3 times 5. Show how the dots in a representation of a trapezoid number can be rearranged into rectangle with more columns than rows. Using inductive reasoning, slow what general formula gives this with trapezoidal number.

Explanation / Answer

#1) Option (C) is correctly chosen by you.

#2) (A) will be the correct option since there the no. of columns is 2 more than the no. of rows.

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