An Arithmetic Progression (AP) is a sequence of numbers where each term after the first is obtained by adding a constant value, called the common difference (\(d\)), to the previous term. APs are foundational in algebra and occur frequently in both academic problems and real-world scenarios.
If the first term is \( a \), then the sequence takes the form:
\[ a, a + d, a + 2d, a + 3d, \dots \]
\[ a_n = a + (n - 1)d \]
\[ S_n = \frac{n}{2}(a + a_n) \]
\[ S_n = \frac{n}{2} \left( 2a + (n - 1)d \right) \]
