(Q8). In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

The number of rose plants in the 1st, 2nd, 3rd, . . ., rows are : 23, 21, 19, . . ., 5

It forms an AP (Why?).

Let the number of rows in the flower bed be n

Then a = , d = – = – , an =

As, an = a + (n – 1) d

We have, = + (n – 1)(– )

i.e., – = (n – 1)(– )

i.e., n =

So, there are rows in the flower bed.