Question

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 total number of trees in the 25 rows.




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Answer 1

Given :

• 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.

To Find :

• Total number of trees in the 25 rows.

Solution :

As Given that ,

1 , 2 , 3...25

$\longmapsto\tt{Common\:Difference\:(d)=2-1=1}$

$\longmapsto\tt{First\:Term\:(a)=1}$

$\longmapsto\tt{nth\:term\:(n)=25}$

Using Formula :

$\longmapsto\tt\boxed{{s}_{n}=\dfrac{n}{2}[2a+(n-1)\times{d}]}$

Putting Values :

$\longmapsto\tt{{s}_{25}=\dfrac{25}{2}[2\times{1}+(25-1)\times{1}}]$

$\longmapsto\tt{{s}_{25}=\dfrac{25}{2}[2+24\times{1}]}$

$\longmapsto\tt{{s}_{25}=\dfrac{25}{{\cancel{2}}}\times{{\cancel{26}}}}$

$\longmapsto\tt{{s}_{25}=25\times{13}}$

$\longmapsto\tt\bf{{s}_{25}=325}$

There are 325 trees in firat 25 rows .

Answer 2

$\Huge\boxed{\textsf{\textbf{\pink{Given\::-}}}}$

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• On the world environment day tree plantation programme was arranged on a land which is triangular in shape.

• Trees are planted such that in first row there is one tree, in second row there are two trees and in third row three trees and so on.

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$\Huge\boxed{\textsf{\textbf{\green{To\:Find\::-}}}}$

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• Total number of trees in 25 rows?

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$\Huge\boxed{\textsf{\textbf{\blue{Solution\::-}}}}$

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$\LARGE\underbrace{\underline{\sf{How\:to\:solve\::-}}}$

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• The number of trees in consecutive rows increase by 1. So, it this is an Arithmetic progression, where d = 1, a = trees in first row = 1 and n = number of rows = 25. We have to find out number of trees in 25 rows? Using well known formula, i.e, formula of sum of first n terms of Arithmetic progression ::

• $\Large\underline{\boxed{\bf{\red{S_{n} = \dfrac{n}{2}\Big[2a + \big(n - 1\big)d\Big]}}}}$

• Where, Sn denotes sum of first n terms, n denotes number of terms, a denotes first term and d denotes common difference.

• Let's solve it!!

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$\underline{\sf{\bigstar\:Putting\:all\:known\:values\::-}}$

$\\ \longrightarrow \:\sf S_{25} = \dfrac{25}{2}\Big[\big(2\big)\big(1\big) + \big(25 - 1\big)\big(1\big)\Big]$

$\\ \longrightarrow \:\sf S_{25} = \dfrac{25}{2}\Big[\big(2\:\times\:1\big) + \big(24\:\times\:1\big)\Big]$

$\\ \longrightarrow \:\sf S_{25} = \dfrac{25}{2}\Big[2 + 24\Big]$

$\\ \longrightarrow \:\sf S_{25} = \dfrac{25}{\cancel{2}}\:\times\:\cancel{26}$

$\\ \longrightarrow \:\sf S_{25} = 25\:\times\:13$

$\\ \longrightarrow \:\boxed{\bf {\purple{S_{25} = 325}}}\:\orange{\bigstar}$

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$\therefore\:{\underline{\sf{Total\:number\:trees\:in\:the\:25\:rows\:is\:{\textit{\textbf{325.}}}}}}$

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$\huge\boxed{\textsf{\textbf{\orange{Explore\:More\::-}}}}$

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• For finding nth term of an arithmetic progression, we use formula ::

• $\LARGE\underline{\boxed{\bf{\purple{a_{n} = a + \Big(n - 1\Big)d}}}}$

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✇ L e a r nㅤm o r eㅤo nㅤb r a i n l y ✇

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$\underline{\sf{\bigstar\:Question\::-}}$

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Divide 56 in four parts in AP such that the ratio of the product of their extremes (1st and 4th) to the product of means (2nd and 3rd) is 5:6.

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$\underline{\sf{\bigstar\:Answer\::-}}$

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https://brainly.in/question/42294457

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