Question

What is the sum of a 22–term arithmetic sequence where the first term is 56 and the last term is –28?

Answer 1

\[
a_1 =56\\
a_2 = 56 -r\\
a_3= 56 -2r\\

a_{22} = 56- 21\ r=-28\\

21 r = 56 + 28=84\\

r= 4


\]

Answer 2

\[
sum = 56 -r + 56-2r +\cdots + 56 - 21 r\\
21(56) -4(1+2 +\cdots +21)=1176-4 (21)(22)/2=252
\]