Answer:
[tex]S_n = (\frac{1}{3} n + \frac{7}{6})[/tex]
Step-by-step explanation:
The partial sum of an arithmetic sequence is: [tex]S{n} = \frac{1}{2} (a_{1}+a_{n})[/tex] where a1 is the first term, an is the nth term, and Sn is the partial sum of up to the nth number in the series. Let's apply the formula.
The first term, a1 is:
a1 = 2/3 (1) + 5/6 = 2/3 + 5/6 = 3/2
The nth term is an = 2/3 n + 5/6
The formula should be:
[tex]S_n = \frac{1}{2} (\frac{3}{2} + \frac{2}{3} n + \frac{5}{6} )\\S_n = (\frac{3}{4} + \frac{2}{6} n + \frac{5}{12})\\S_n = (\frac{1}{3} n + \frac{7}{6})[/tex]
