If the (8)th term of an AP is (x+19) and the (20)th term is (x+91), what is the (35)th term in terms of (x)?

Correct answer: \(x+181\)

There are 12 term-intervals between the 8th and the 20th terms. Hence, \(12d=(x+91)-(x+19)=72\), so \(d=6\). From the 20th term to the 35th term, there are 15 intervals; therefore, \(a_{35}=x+91+15\times6=x+181\). Thus, \(x+181\) is correct. \(x+175\) would result from incorrectly using only 14 intervals. Exam tip: first find \(d\) from the two given terms, then count the term-intervals from the nearer known term.