If the (29)th term of the AP (u-9,u-1,u+7,\ldots) is (295), what is the value of (u)?

Correct answer: 80

The difference between consecutive terms is \(8\), so the first term is \(a=u-9\) and the common difference is \(d=8\). Using \(a_n=a+(n-1)d\), \(295=(u-9)+28\times8=u+215\). Hence, \(u=80\). If \(u=78\), the 29th term would be \(293\), so it is not correct. Exam tip: for the \(n\)th term, use \(n-1\) common differences, not \(n\).