The participants are arranged in rows:
Row 1: 34 participants
Row 2: 31 participants
Row 3: 28 participants
Last row: 16 participants
The decrease between consecutive rows:
34 - 31 = 3
31 - 28 = 3
Each row has 3 fewer participants than the previous row. This forms an arithmetic sequence with common difference d=−3.
For an arithmetic sequence:
an=a1+(n−1)×d
Where:
- an=16 (last row)
- a1=34 (first row)
- d=−3 (common difference)
- n= number of rows
Substituting the values:
16=34+(n−1)×(−3)
16=34−3(n−1)
16=34−3n+3
16=37−3n
−21=−3n
n=7
Therefore, there are 7 rows in the seminar room.