An arithmetic series is a series in which each term is increased or decreased by a constant difference. The constant difference is known as common difference of the series and generally represented by \(‘d’\). For example the series 

\(2 + 6 + 10 + 14 + 18……..\) is in A.P., since the difference between successive terms is a constant equal to 4.

\({n^{th}}\) term 

If the first term of the series is \(a\),

Second term will be \(a + d\)

Third term will be \(a + 2d\)

Fourth term will be \(a + 3d\)

Similarly, \({n^{th}}\) term will be \(a + (n - 1)d\) 

\({n^{th}}\) term of the series is represented by \({T_n}\), where 

\[{T_n} = a + {\rm{ }}\left( {n--{\rm{ }}1} \right)d\]