The (n)th term of the AP (73,68,63,\ldots) is (-12). What is (n)?

Correct answer: (18)

The direct answer is C, 18. The first term is 73 and the common difference is \(68-73=-5\). Use \(a_n=a+(n-1)d\): \(-12=73+(n-1)(-5)\). Subtracting 73 gives \(-85=-5(n-1)\); dividing by -5 gives \(17=n-1\), so \(n=18\). Option A, 16, would give the term \(73+15(-5)=-2\), not -12. Option B, 17, corresponds to one fewer step and gives -7. Option C, 18, gives \(73+17(-5)=73-85=-12\), so it is correct. Option D, 19, takes one extra step and gives -17. The common mistake is to use n instead of n-1 in the nth-term formula. Check the answer by substituting n=18 into the formula.