In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.

Correct answer: (14)

Direct answer: B, 14. In an AP, the sum of the first n terms is \(S_n=\frac{n}{2}(a+l)\), where a is the first term and l is the nth, or last, term of those n terms. Here \(S_{20}=740\), \(n=20\), and \(l=60\). Substitute: \(740=\frac{20}{2}(a+60)=10(a+60)\). Divide by 10: \(74=a+60\). Subtract 60: \(a=14\). Thus B is correct. Option A, 10, would give sum \(10(10+60)=700\), not 740. Option C, 18, would give \(10(18+60)=780\). Option D, 22, would give \(10(22+60)=820\). The given 20th term is used as the last term because the sum ends at the 20th term. Memory cue: when sum and last term are known, use \(S_n=\frac n2(a+l)\).