In a flower bed, there are 43 rose plants in the first row, 41 in the second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?

The no of rose plants in each row can be arranged in the form of an AP as 43, 41, 39, …, 11.

Here, First term = a = 43

Common difference = d = 41 - 43 = - 2

No of terms in the AP = No of rows in the flower bed.

∴ 11 = a + (n - 1)d

⇒ 11 = 43 + (n - 1)(-2)

⇒ 11 - 43 = - 2n + 2

⇒ 11 - 43 - 2 = - 2n

⇒ 2n = 34

⇒ n = 17

∴ No of rows in the flower bed = 17