In an AP, (a_3+a_8=76) and (a_{13}=92). What is (a_{27})?

Correct answer: 192.8

Let the first term be \(a\) and the common difference be \(d\). Then \(a_3+a_8=(a+2d)+(a+7d)=2a+9d=76\), while \(a_{13}=a+12d=92\). Multiplying the second equation by 2 gives \(2a+24d=184\). Subtracting the first equation gives \(15d=108\), so \(d=7.2\). Hence \(a=92-12(7.2)=5.6\), and \(a_{27}=a+26d=5.6+26(7.2)=192.8\). The nearby distractor 196 does not satisfy the given conditions. Exam tip: first convert every stated AP term or sum into equations in \(a\) and \(d\).