If the (6)th term of an AP is (x+11) and the (15)th term is (x+65), what is the (27)th term in terms of (x)?

Correct answer: \(x+137\)

The difference between the 15th and 6th terms is \(9d\). Thus, \(9d=(x+65)-(x+11)=54\), so \(d=6\). From the 15th term to the 27th term, there are 12 common differences. Hence, \(a_{27}=x+65+12\times6=x+137\). Therefore, option B is correct. \(x+131\) would result from incorrectly using 11 common differences. Exam tip: Count the difference in term numbers carefully when moving between two AP terms.