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 :

The correct answer is (A) 10.

Step-by-step arithmetic progression solution:

• The number of rose plants in successive rows forms an Arithmetic Progression (AP): $23, 21, 19,$$\dots$, 5.
• First term ($a$) = 23, Common difference ($d$) = $21 - 23 = -2$, and Last term ($a_n$) = 5.
• Using the general term formula: $a_n = a + (n - 1)d$.
• $5 = 23 + (n - 1)(-2)$$\implies$ 5 - 23 = -2(n - 1) $\implies$ -18 = -2(n - 1).
• $n - 1 = 9$$\implies$ n = 10.
• Therefore, the flower bed contains 10 rows.