Asked by alicia
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
Answers
Answered by
Damon
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
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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