Question

What is the sum of a 12–term arithmetic sequence where the last term is 13 and the common difference is –10?

Answer 1

if we knew a1 we would be set

Answer 2

a12 = a1 +d(11)

a12 - d(11) = a1

Answer 3

\[S_{12}=\frac{n(a_1+a_{12})}{2}\]
\[S_{12}=\frac{n(a_{12}-d(11)+a_{12})}{2}\]
\[S_{12}=\frac{n(2a_{12}-d(11))}{2}\]