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P-1 Arithmetic Progression — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-1 Arithmetic Progression4 Marks
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.
✓

Answer

First term a = 1
Second term t1 = 2
Third term t3 = 3
Common difference d = t3 – t2 = 3 – 2 = 1
We need to find total number of trees when n = 25
Thus, By using sum of nth 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
$\begin{array}{l}
a=\text { first term } \\
d=\text { common difference } \\
S_n=\text { sum of } n \text { terms }
\end{array}$
We need to find $S_{25}$
Thus, on substituting the given value in formula we get,
$\begin{array}{l}
\Rightarrow S_{25}=\frac{25}{2}[2 \times 1+(25-1) \times 1] \\
\Rightarrow S_{25}=\frac{25}{2}[2+24] \\
\Rightarrow S_{25}=\frac{25}{2} \times 2 \times[1+12] \\
\Rightarrow S_{25}=25 \times 13=325
\end{array}$

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