On the world environment day tree plantation programme was arrang… - Vidyadip

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.

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Answer

First term a = 1
Second term $\mathrm{t}_1=2$
Third term $\mathrm{t}_3=3$
Common difference $d=t_3-t_2=3-2=1$
We need to find total number of trees when $n=25$
Thus, By using sum of $n^{\text {th }}$ term of an A.P. we will find it's sum
$S_n=\frac{n}{2}[2 a+(n-1) d]$
Where, $n=$ no. of terms
$a=$ first term
$\mathrm{d}=$ common difference
$S_n=$ sum of $n$ terms
We need to find $\mathrm{S}_{25}$
Thus, on substituting the given value in formula we get,
$\Rightarrow S_{25}=\frac{25}{2}[2 \times 1+(25-1) \times 1] $
$ \Rightarrow S_{25}=\frac{25}{2}[2+24] $
$ \Rightarrow S_{25}=\frac{25}{2} \times 2 \times[1+12] $
$ \Rightarrow S_{25}=25 \times 13=325$

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