In a flower bed, there are 23 rose plants in the first row, 21 in the

1.	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?
Answer» 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 = 23, d = 21 – 23 = – 2, a_n = 5 As, a_n = a + (n – 1) d We have, 5 = 23 + (n – 1)(– 2) i.e., – 18 = (n – 1)(– 2) i.e., n = 10 So, there are 10 rows in the flower bed.

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?

Answer»

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 = 23, d = 21 – 23 = – 2, a_n = 5

As, a_n = a + (n – 1) d

We have, 5 = 23 + (n – 1)(– 2)

i.e., – 18 = (n – 1)(– 2)

i.e., n = 10

So, there are 10 rows in the flower bed.