If the (25)th term of the AP (t-8,t-1,t+6,\ldots) is (230), what is the value of (t)?

Correct answer: 70

The difference between consecutive terms is \(7\), so the first term is \(a=t-8\) and the common difference is \(d=7\). The \(25\)th term is \(a_{25}=a+24d\). Thus, \(230=(t-8)+24\times7=t+160\), giving \(t=70\). If \(t=66\), the \(25\)th term would be \(226\), so it is not correct. Exam tip: in the formula for the \(n\)th term, multiply \(d\) by \(n-1\), not by \(n\).