SOLUTION: In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n?

Question 1020716: In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n?
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a(m) = a(1) + (m-1)d = n
a(n) = a(1) + (n-1)d = m
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Subtract to get:
(m-1)d-(n-1)d = n-m
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md-d-nd-d = n-m
(m-n)d-2d = n-m
----
(m-n-2)d = n-m
----
d = (n-m)/(m-n-2)
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Solve for "a(1)"::
a(1) = m +(1-n)d
a(1) = m + (1-n)[(n-m)/(m-n-2)]
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Cheers,
Stan H.
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