If the (7)th term of an AP is (x+13) and the (18)th term is (x+90), what is the (32)nd term in terms of (x)?

Correct answer: \(x+188\)

For an AP, \(a_{18}-a_7=(18-7)d\). Thus, \((x+90)-(x+13)=11d\), so \(77=11d\) and \(d=7\). Now \(a_{32}=a_{18}+(32-18)d=x+90+14\times7=x+188\). Therefore, option B is correct. Choosing \(x+195\) would incorrectly use a gap of 15 terms, whereas the gap from the 18th to the 32nd term is 14. Exam tip: always subtract the term numbers to find the number of common differences between two terms.