how do i solve the sum of the first two terms of an arithmetic sequence is 16. the sum of the second and third term is 28. determine the first three terms, algebraically

Answer 1

a1 + a2 = 16

a2 + a3 = 28

and since it is an arithmetic sequence
a2 - a1 = a3 - a2
or
a2 = (a1+a3)/2 (the average of course)

substitute back
a1 + (a1+a3)/2 = 16
(a1+a3)/2 + a3 = 28

solve those two equations for a1 and a3, then go back and get a2