The Given Sequence is an Arithmetic Sequence with First term = -19
⇒ a = -19
Second term is -13
We know that Common difference is Difference of second term and first term.
⇒ Common Difference (d) = -13 + 19 = 6
We know that Sum of n terms is given by : [tex]S_n = \frac{n}{2}(2a + (n - 1)d)[/tex]
Given n = 63 and we found a = -19 and d = 6
[tex]\implies S_6_3 = \frac{63}{2}(2(-19) + (63 - 1)6)[/tex]
[tex]\implies S_6_3 = \frac{63}{2}(-38 + (62)6)[/tex]
[tex]\implies S_6_3 = \frac{63}{2}(-38 + 372)[/tex]
[tex]\implies S_6_3 = \frac{63}{2}(-38 + 372)[/tex]
[tex]\implies S_6_3 = \frac{63}{2}(334)[/tex]
[tex]\implies S_6_3 = {63}(167) = 10521[/tex]
The Sum of First 63 terms is 10521
