math sequences and series
posted by alicia on .
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

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