Respuesta :
The sequence 2,7,12,... given is an arithmetic progression. This is because it has a common difference.
Given:
first term, a = 2
common difference, d = second term - first term = 7 - 2 = 5
d = 5
n = 38
The sum of an arithmetic progression is given by;
[tex]\begin{gathered} S_n=\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ S_{38}=\frac{38}{2}\lbrack2(2)+(38-1)5\rbrack \\ S_{38}=19\lbrack4+37(5)\rbrack \\ S_{38}=19\lbrack4+185\rbrack \\ S_{38}=19(189) \\ S_{38}=3591 \end{gathered}[/tex]Therefore, the sum of the first 39 terms of the series is 3,591
