Sir please give me a detailed solution of this question in which we have been asked to calculate the number of rows, if 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.

RS Aggarwal, class 10, chapter 5A, question no 46

Number of rose plants in first, second, third rows…. are 43, 41, 39…respectively.

There are 11 rose plants in the last row

So, it is an AP. i.e. 43, 41, 39 …. 11

a = 43, d = 41 – 43 = -2, l = 11

Let nth term be the last term

= a + (n – 1)d

11=43+(n-1)(-2)

43 – 2n + 2 = 11

or 2n = 45 – 11 = 34

n =34/2

= 17

Hence, there are 17 rows in the flower bed.