If (3,8,13,18,\ldots) is written in reverse order, what happens to the sign of the common difference?

Correct answer: It becomes negative

The direct answer is option C: the common difference becomes negative. In the original sequence, moving forward gives
\(8-3=5\),
\(13-8=5\), and
\(18-13=5\), so the original common difference is
\(d=5\). Reversing the order gives
\(18,13,8,3,\ldots\). Now consecutive differences are
\(13-18=-5\),
\(8-13=-5\), and
\(3-8=-5\). Thus the new common difference is
\(-5\), which is negative. Option A is wrong because the direction has reversed, so +5 does not describe the new order. Option B is wrong because the terms are not equal. Option C is correct. Option D is wrong because a constant difference still exists. Memory cue: reversing an AP changes
\(d\) to
\(-d\).