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

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1. anonymous

For the first series, $$S_1=1$$ and $$S_2=1+5=S_1+5=6$$ (a common difference of 5 between successive terms). Next, $$S_3=6+5=S_2+5=S_1+2(5)=11$$. Continuing the pattern, you can establish that\begin{align*}S_n&=S_{n-1}+5\\&=S_{n-2}+(2)5\\&=\cdots\\&=S_2+(n-2)5&\\&=S_1+(n-1)5\end{align*} Then $$S_{12}=S_1+(12-1)5=\cdots$$. You can use the same reasoning to figure out the second problem.