Discussion
In a flower bed, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and 5 rose plants in the last row. The number of rows in the flower bed is :
Answer: A
The flower bed has 10 rows.
The rows form an arithmetic progression with first term 23 and common difference -2, ending at 5. The number of terms is:
\[ \begin{aligned} n &= \frac{\text{first} - \text{last}}{\text{difference}} + 1 \\ &= \frac{23 - 5}{2} + 1 = 9 + 1 = 10 \end{aligned} \]
Check: 23, 21, 19, 17, 15, 13, 11, 9, 7, 5 is ten rows. Forgetting the +1 gives 9; 15, 17 and 18 do not fit the sequence.
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