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If <em>a</em> is the first term of an AP with common difference -2, then the first several terms are
<em>a</em>, <em>a</em> - 2, <em>a</em> - 4, <em>a</em> - 6, <em>a</em> - 8, …
with <em>n</em>-th term <em>a</em> - 2 (<em>n</em> - 1).
The sum of the first <em>n</em> terms is equal to the sum of the first 3<em>n</em> terms :
We have
so that in the previous equation, the sums reduce to
Solve for <em>a</em> :
Now if <em>a</em> = 27, we have
27 = 4<em>n</em> - 1
28 = 4<em>n</em>
<em>n</em> = 7
as required.