# math sequences and series

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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

• math sequences and series -

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

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