Which formula represents the partial sum of the first n terms of the series: 2 + 6 + 10 + ... + (4n - 1)?A) 4n^2 + 2n B) 4n^2 + 1/2n C) 2n^2 + 2n D) 2n^2 + 1/2n Will give brainlist and 15 points to correct answer. Please help.

The formula which represents the partial sum of the first n terms of the series is [tex]2n^{2}+\frac{1}{2}n[/tex] ⇒ DStep-by-step explanation:The sum of nth terms of the arithmetic series is [tex]S_{n}=\frac{n}{2}[a+l][/tex] , wherea is the first terml is the last term∵ The first n terms of the series are 2 + 6 + 10 + ......... + (4n - 1)∵ 6 - 2 = 4 and 10 - 6 = 4∴ There is a constant difference between the consecutive terms∴ The series is arithmetic∴ The sum of nth terms is [tex]S_{n}=\frac{n}{2}[a+l][/tex]∵ The first term is 2∴ a = 2∵ The last term is (4n - 1)∴ l = (4n - 1)- Substitute these values in the rule∴ [tex]S_{n}=\frac{n}{2}[2+(4n-1)][/tex]∴ [tex]S_{n}=\frac{n}{2}[2+4n-1][/tex]- Add like terms in the right hand side∴ [tex]S_{n}=\frac{n}{2}[4n+1][/tex]- Simplify it∴ [tex]S_{n}=(\frac{n}{2})(4n)+(\frac{n}{2})(1)[/tex]∴ [tex]S_{n}=2n^{2}+\frac{1}{2}n[/tex]The formula which represents the partial sum of the first n terms of the series is [tex]2n^{2}+\frac{1}{2}n[/tex]Learn more:You can learn more about the sequences in brainly.com/question/7221312#LearnwithBrainly