Stacks and rows

A hall has seats in rows. Row 1 has 3 seats. Each row has 2 more than the row before. There are 4 rows. Count every seat.

Rule: read the first term and the step from the story. The step must be the same every row. Then decide — does the question want one term, or the whole total?

A bigger hall has 12 seats in row 1. Each row after has 4 more seats. It has 15 rows. Row 15 is 14 steps after row 1. So row 15 holds 12 + 14 × 4 = 68 seats. All 15 rows hold 15/2 × (12 + 68) = 600 seats.

A log pile has 15 logs at the bottom. Each row up has one fewer log, down to 1 on top. How many logs in the pile?

Here the story does not give the number of rows. From 15 down to 1 in steps of 1 is 15 rows. The first term is 15 and the last is 1. So use n/2 (a + l). The total is 15/2 × (15 + 1) = 120 logs.

Pick a stack. Count it row by row.