In an AP, (a_{12}=54) and (a_{20}=94). What is the first term?

Correct answer: -1

For an AP, \(a_n=a+(n-1)d\). Thus, \(a_{20}-a_{12}=8d=94-54=40\), so \(d=5\). Using \(a_{12}=a+11d\), we get \(54=a+11\times5\), hence \(a=-1\). The option 0 would result from subtracting only 10 common differences from \(a_{12}\), but the 12th term is 11 common differences after the first term. Exam tip: always use \((n-1)d\) for the \(n\)th term.