In a seminar room, there are 34 participants in the first row, 31 in the second, 28 in the third, and so on. There are 16 participants in the last row. How many rows are there in the seminar room?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7
The rows go down by 3 each time (34, 31, 28, …), so the numbers form an arithmetic progression with first term \(a=34\) and common difference \(d=-3\). The \(n\)th term is \(a+(n-1)d\), and the last row has 16.
The equation (the last row, 16, is the \(n\)th term):
\(34+(n-1)(-3)=16\)
Finding \(n\) (each row after the first has 3 fewer, so the drop from 34 to 16 is \(n-1\) steps of 3):
\((n-1)\times3=34-16=18\)
\(n-1=6\)
\(n=7\), so there are 7 rows (34, 31, 28, 25, 22, 19, 16)