Arithmetic Sequences

Let $T(1)$, $T(2)$, …, $T(n)$ be an arithmetic sequence and $d$ be the common difference. For natural number $n$ and $n>1$,

1. The general term
   \begin{equation*}
   T(n)=T(1)+(n-1)d
   \end{equation*}

2. The sum of the first $n$ terms
   \begin{equation*}
   S(n)=\frac{n}{2}[2T(1)+(n-1)d]
   \end{equation*}
   or
   \begin{equation*}
   S(n)=\frac{n}{2}[T(1)+T(n)]
   \end{equation*}

Same Topic:

Fibonacci Sequence Geometric Sequences Square Numbers Triangle Numbers