These are arithmetic sequences.
The nth term of an arithmetic sequence:
[tex]a_n=a_1+d(n-1)[/tex]
The sum of n terms of an arithmetic sequence:
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]
a₁ - the first term
d - the common difference
1)
[tex]1,6,11,16,... \\ \\
a_1=1 \\
d=a_2-a_1=6-1=5 \\
a_{12}=1+5(12-1)=1+5 \times 11=1+55=56 \\ \\
S_{12}=\frac{12(1+56)}{2}=\frac{12 \times 57}{2}=6 \times 57=342 \\
\boxed{S_{12}=342}[/tex]
2)
[tex]-6,-4,-2,0,... \\ \\
a_1=-6 \\
d=a_2-a_1=-4-(-6)=-4+6=2 \\
a_{22}=-6+2(22-1)=-6+2 \times 21=-6+42=36 \\ \\
S_{22}=\frac{22(-6+36)}{2}=\frac{22 \times 30}{2}=11 \times 30=330 \\
\boxed{S_{22}=330}[/tex]
