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. ​

Answer 1

Answer:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25= 325

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

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

$\\ \longrightarrow \: \sf \: S_{25} = \dfrac{25}{2} \big ]$

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

$\\ \longrightarrow \: \sf \: </p><p>S_{25} = \dfrac{25}{2} \big \: [ 2 + 24 \big]$

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

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

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

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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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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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$\underline {\sf {\bigstar \: \: {answer given by : - }}}$

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