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Question
On the world environment day tree plantation programme was arranged on a land which is triangular in shape. Trees are planted such that in the first row there is one tree, in the second row there are two trees, in the third row three trees and so on. Find the total number of trees in the 25 rows.
Solution
Total number of rows = 25
Number of trees in first row = 1
Number of trees in second row = 2
Number of trees in third row = 3
Total number of trees = 1 + 2 + 3 + ..... + upto 25 rows
Here,
a = 1
d = 1
n = 25
Now,
\[S_n = \frac{n}{2}\left( 2a + \left( n - 1 \right)d \right)\]
\[ S_{25} = \frac{25}{2}\left( 2a + \left( 25 - 1 \right)d \right)\]
\[ = \frac{25}{2}\left( 2\left( 1 \right) + 24\left( 1 \right) \right)\]
\[ = \frac{25}{2}\left( 2 + 24 \right)\]
\[ = \frac{25}{2}\left( 26 \right)\]
\[ = 25 \times 13\]
\[ = 325\]
Hence, the total number of trees are 325.
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