In a school, a plantation program was arranged on the occasion of world environment day, on a ground of triangular shape. The trees are to be planted as shown in the figure. One plant in the first row, two in the second row, three in the third row and so on. If there are 25 rows then find the total number of plants to be planted.

10. In a school, a plantation program was arranged on the occasion of world environment day, on a ground of triangular shape. The trees are to be planted as shown in the figure. One plant in the first row, two in the second row, three in the third row and so on. If there are 25 rows then find the total number of plants to be planted.

Sol. The number of trees in each row upto the 25th row are as follows : 1, 2, 3, 4, ...........

These no. of trees planted in each row forms an A.P. with

No. of trees in first row (a) = 1

Difference between no. of trees planted in two successive rows (d) = 1

No. of rows (n) = 25

Sn = n/2[2a + (n – 1) d]

∴  S25 = 25/2[2 (1) + (25 – 1) 1]

∴  S25 = 25/2[2 + 24]

∴  S25 = 25/2 (26)

∴  S25 = 25 (13)

∴  S25 = 325

∴  325 trees were planted in 25 rows.