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The first term is a, the second term is a + d, the third, a + 2d, etc.
So the sum of the first 6 terms is
. The 15 comes from
So our first equation is
The second term is
and the fifth term is
, so the second equation is:
, which simplifies to
Add the two equations, since the coefficients on the a terms are already additive inverses
Substitute this value for d into the first equation: