the arroyos are planning to build a brick patio that approximates the shape of a trapezoid. the shorter base of the trapezoid needs to start with a row of 5 bricks, and each row must increased by 2 bricks on each side until there are 35 rows.
how many bricks do the arroyos need?

Question

the arroyos are planning to build a brick patio that approximates the shape of a trapezoid. the shorter base of the trapezoid needs to start with a row of 5 bricks, and each row must increased by 2 bricks on each side until there are 35 rows.
how many bricks do the arroyos need?

anonymous · Answer

The rows are an arithmetic sequence: 5, 7, 9, 11, ..., 35.  Hint:  If$$S=5+7+9+11+\cdots+35$$then$$2S=(5+35)+(7+33)+(9+31)+(11+29)+\cdots + (35+5).$$Note how all the values in the parenthesis are the same.  This scheme can let you reason out $S$.