Suppose y = 48 + 3(2n - 1) is an explicit representation of an arithmetic sequence for integer values n ≥ 1. Find the xth partial sum of the series, as a quadratic function, where x represents the term number.
The formula of the sum of the arithmetic sequence: [tex]S_n=\dfrac{a_1+a__n}{2}\cdot n[/tex] calculate: [tex]a_1=48+3(2\cdot1-1)=48+3=51[/tex] substitute [tex]S_n=\dfrac{51+48+3(2n-1)}{2}\cdot n=\dfrac{99+6n-3}{2}\cdot n=\dfrac{96+6n}{2}\cdot n=3n^2+48n[/tex] Your answer is: [tex]\boxed{f(x)=3x^2+48x}[/tex]
