Question

In a school, a plantation programme 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.

• A. 320
• B. 322
• C. 325
• D. 330

Answer 1

The correct option is C 325

Trees are to be planted in each row are as follows
1,2,3,.........
This sequence forms an AP with first term a=1, common difference d=1.
Given, number of terms n=25.
Total trees in 25 rows=$S_{25}$
Since, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow S_{25}=\frac{25}{2}[2\times 1+(25-1\left)1\right]$
$\Rightarrow S_{25}=\frac{25}{2}[2+24]$
$\Rightarrow S_{25}=25\times 13$
$\Rightarrow S_{25}=325$
$\therefore$ Total trees in 25 rows $S_{25}$=325