Question

1)Find S12 for 1 + 6 + 11 + 16 +… 2)Find S22 for -6 + (-4) + (-2) + 0 … thanks for your help!

Answer 1

These are arithmetic sequences.
The nth term of an arithmetic sequence:

`a_n=a_1+d(n-1)`
The sum of n terms of an arithmetic sequence:

`S_n=(n(a_1+a_n))/(2)`
a₁ - the first term
d - the common difference

1)

`1,6,11,16,... \\ \\ a_1=1 \\ d=a_2-a_1=6-1=5 \\ a_(12)=1+5(12-1)=1+5 * 11=1+55=56 \\ \\ S_(12)=(12(1+56))/(2)=(12 * 57)/(2)=6 * 57=342 \\ \boxed{S_(12)=342}`

2)

`-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 * 21=-6+42=36 \\ \\ S_(22)=(22(-6+36))/(2)=(22 * 30)/(2)=11 * 30=330 \\ \boxed{S_(22)=330}`