Download App

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,
$\begin{array}{l}
\Rightarrow S_{25}=\frac{25}{2}[2 \times 1+(25-1) \times 1] \\
\Rightarrow S_{25}=\frac{25}{2}[2+24] \\
\Rightarrow S_{25}=\frac{25}{2} \times 2 \times[1+12] \\
\Rightarrow S_{25}=25 \times 13=325
\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from P-1 Arithmetic Progression→P-1 Arithmetic Progression — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

The height of a right circular cone is 20cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be $\frac{1}{8}$ of the volume of the given cone, then at what height above the base is the section made?
→
A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, If he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.
→
The first and the last terms of an A.P. are $7$ and $49$ respectively. If sum of all its terms is $420$, find its common difference.
→
Ramesh travels 760km to his home partly by train and partly by car. He takes 8 hours if he travels 160km. by train and the rest by car. He takes 12 minutes more if the travels 240km by train and the rest by car. Find the speed of the train and car respectively.
→
Prove the following trigonometric identities.
If $\cos\text{A}+\cos^2\text{A}=1,$ prove that $\sin^{12}\theta+\sin^{10}\theta+3\sin^8\theta+\sin^6\theta+2\sin^4\theta+2\sin^2\theta-2=1.$
→
Determine a point which divides a line segment of length 12cm internally in the ratio 2 : 3. Also justify your construction.
→
Show that the following points are the vertices of a square:
A(6, 2), B(2, 1), C(1, 5) and D(5, 6)
→
A wizard having powers of mystic in candations and magical medicines seeing a cock, fight going on, spoke privately to both the owners of cocks. To one he said, if your bird wins, than you give me your stake-money, but if you do not win, I shall give you two third of that'. Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only 12 gold coins. Find the the stake of money each of the cock-owners have.
→
In the adjoining figure, seg AB || side DC, $OD =x OB =x-3, OC$ $=x-5, OA =3 x-19$ Find the value of $x$.
Image
→
Find the sum of odd natural numbers from 1 to 101.
→