Arithmetic Progression
\(a, \: a + b, \: a + 2b, \: a + 3b, \: \dotso \)
\(T_n = a + (n - 1)b\)
\(T_n - T_{n - 1} = b\)
\(S_n = \dfrac{n}{2} \:.\: \left[a + T_n \right]\)
\(S_n = \dfrac{n}{2} \:.\: \left[2a + (n - 1)b \right] \)
Exercise
\(a, \: a + b, \: a + 2b, \: a + 3b, \: \dotso \)
\(T_n = a + (n - 1)b\)
\(T_n - T_{n - 1} = b\)
\(S_n = \dfrac{n}{2} \:.\: \left[a + T_n \right]\)
\(S_n = \dfrac{n}{2} \:.\: \left[2a + (n - 1)b \right] \)