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.

Answer 1

We have:
t₁ = 1 tree in the 1^st row
t₂ = 2 trees in the 2^nd row
t₃ = 3 trees in the 3^rd row and so on.
Therefore, the numbers of trees in the rows are in an A.P.
We have:
First term, a = t₁ = 1
Common difference, d = t₂ – t₁ = 2 – 1 = 1
Now,
To find the total number of trees in all 25 rows, we need to find the sum of the first 25 terms of the
A.P.
We know that the sum of n terms of an A.P is $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$.
Thus, taking a = 1, d = 1 and n = 25, we get:
$$\begin{gathered} S_{25}=\frac{25}{2}\left[2\times 1+(25-1)1\right] \\ =\frac{25}{2}\left[2+24\right] \\ =\frac{25}{2}\times 26 \\ =25\times 13 \\ =325 \end{gathered}$$

Thus, there are 325 trees in 25 rows.