Input data
11, 19, 27
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. An arithmetic sequence can be defined by an explicit formula in which an = d (n - 1) + c, where d is the common difference between consecutive terms, and c = a1.
Procedure
d = 19 - 11 = 8
d = 27 - 19 = 8
a1 = 11
[tex]a_n=11+8(n-1)[/tex]for n = 41
To find the sum of the first n terms of an arithmetic series use the formula, n terms of an arithmetic sequence use the formula,
[tex]\begin{gathered} S_n=\frac{n(a_1+a_n)}{2} \\ \end{gathered}[/tex]a41 = 11+8(41-1)
a41 = 11+8*40
a1 = 331
[tex]\begin{gathered} S_{41}=\frac{41(11+331)}{2} \\ S_{41}=\frac{41(342)}{2} \\ S_{41}=6642 \end{gathered}[/tex]