What will be the (16)th term of the AP (12,18,24,30,\ldots)?

Correct answer: (102)

The direct answer is option B, 102. In an arithmetic progression, the difference between consecutive terms is constant. Here, the first term is a=12 and the common difference is d=18-12=6. The nth-term rule is \(a_n=a+(n-1)d\), because the first term has zero added differences. Therefore, \(a_{16}=12+(16-1)6=12+15\times6=12+90=102\). Option A, 96, is wrong because it does not result from the correct fifteenth difference. Option B, 102, is correct because it uses the first term and 15 equal jumps of 6. Option C, 108, is too large and would require 16 jumps after the first term. Option D, 90, is too small. Remember: for the nth term, always use n-1, not n, common differences.