Stacks and rows
Show on a big screenA 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.
- Row 1 has 3 seats.
- Row 2 has 5 seats — 2 more than row 1.
- Row 3 has 7 seats. Row 4 has 9 seats.
- 3 + 5 + 7 + 9 = 24 seats in all.
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.
| Move | The hall | The log pile |
|---|---|---|
| First term | 12 | 15 |
| Step | +4 | −1 |
| Term, or total? | both — 68, then 600 | total — 120 |
Pick a stack. Count it row by row.
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