You can tell this is an arithmetic sequence because it is a list of terms beginning with -19 that increase by 6 each term. Because of this, we can use the formula for the sum of an arithmetic sequence, which is:
[tex]S = \dfrac{n}{2}[2 a_1 + d(n - 1)][/tex]
- [tex]n[/tex] is the number of terms in the sequence
- [tex]a_1[/tex] is the starting term
- [tex]d[/tex] is the common difference among the terms
In this case, we can see that [tex]n = 63[/tex], [tex]a_1 = -19[/tex], and [tex]d = 6[/tex]. Thus, we can use the formula:
[tex]S = \dfrac{63}{2} [2(-19) + 6(62)] = 10,521[/tex]
Our answer is 10,521.
