In the AP (-92,-69,-46,\ldots), what is the first term greater than (900)?

Correct answer: 920

Here, the first term is \(a=-92\) and the common difference is \(d=23\). Thus, \(a_n=a+(n-1)d=-92+23(n-1)=23n-115\). From \(23n-115>900\), we get \(n>44.13\), so the smallest integer value is \(n=45\). Hence, \(a_{45}=920\), which is the first term greater than 900. The close distractor 897 is the 44th term, so it is still less than 900. Exam tip: for the first term greater than a number, solve the inequality and take the next integer value of \(n\).