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 nth TERM of Arithmetic progression ::

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

S

n

=

2

n

[2a+(n−1)d]

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

Let's solve it!!

\:

\underline{\sf{\bigstar\:PUTTING\:all\:known\:values\::-}}

★Puttingallknownvalues:−

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

⟶S

25

=

2

25

[(2)(1)+(25−1)(1)]

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

⟶S

25

=

2

25

[(2×1)+(24×1)]

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

⟶S

25

=

2

25

[2+24]

\begin{gathered}\\ \longrightarrow \:\sf S_{25} = \dfrac{25}{\cancel{2}}\:\times\:\cancel{26}\end{gathered}

⟶S

25

=

2

25

×

26

\begin{gathered}\\ \longrightarrow \:\sf S_{25} = 25\:\times\:13\end{gathered}

⟶S

25

=25×13

\begin{gathered}\\ \longrightarrow \:\boxed{\bf {\purple{S_{25} = 325}}}\:\orange{\bigstar}\end{gathered}

⟶

S

25

=325

★