If
[tex]S=14+20+26+\cdots+1232+1238+1244[/tex]
then
[tex]S=1244+1238+1232+\cdots+26+20+14[/tex]
We can pair terms in the same positions to get
[tex]2S=(14+1244)+(20+1238)+\cdots+(1238+20)+(1244+14)[/tex]
[tex]2S=\underbrace{1258}_{206\text{ times}}[/tex]
[tex]\implies S=\dfrac{206\cdot1258}2=\boxed{129,574}[/tex]
We know there are 206 copies of 1258 being added because
[tex]14+6(n-1)=1244\implies n=206[/tex]
