find out a couple of words from the extract that mean almost the same write the meanings nine gold medals
Answers
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
★