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?

7

The correct answer is Option (1) → 7

To find the number of rows in the seminar room, we can treat the number of participants in each row as an Arithmetic Progression (AP).

1. Identify the given values

• First term ($a$): 34 (participants in the first row)

• Common difference ($d$): $31-34=-3$

• Last term ($a^n$): 16 (participants in the last row)

2. Apply the formula for the $n^{th}$ term

The formula for the $n^{th}$ term of an AP is: $$a^n=a+(n-1)d$$

Where $n$ represents the total number of rows. Substitute the known values into the formula: