In a row of students, there are 27 students in the first row, 24 in the second, 21 in the third, and so on. There are 6 students in the last row. How many students are there in all the rows?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 132
Each row has 3 students fewer than the row before, so the numbers 27, 24, 21, ..., 6 form an arithmetic progression with first term \(a=27\) and common difference \(d=-3\). The number of rows comes from the last term, and the total from the sum formula \(S_n=\frac{n}{2}(\text{first}+\text{last})\).
Number of rows: \(27+(n-1)(-3)=6\), so \(n-1=7\) and \(n=8\)
Total: \(\displaystyle S_8=\frac{8}{2}(27+6)=4\times33=132\)