Question

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

[Hint: Take a = 43, d = –2 and `l` = 11.
            a + (n – 1)d = l ⇒ 43 + (n – 1) × (–2) = 11 ⇒ 2n = 34 ⇒ n = 17.
            Sun = `17/2(43 + 11) = (17 xx 27) = 459.`]

Answer 1

The rows form an AP: 43, 41, 39, ...

Here $$a = 43, \ d = -2, \ l = 11$$. 

Let the number of rows be n.

$$l = a + (n - 1)d$$

$$\Rightarrow 43 + (n - 1)(-2) = 11$$

$$\Rightarrow 45 - 2n = 11$$

$$\Rightarrow n = 17$$ 

Total plants = $$S_{17}$$

$$= \frac{17}{2}(43 + 11)$$

$$= 17(27)$$

$$= 459$$