In the AP (24,33,42,\ldots), how many terms are less than (400)?

Correct answer: 42

Here, the first term is 24 and the common difference is 9. Therefore, \(a_n=24+9(n-1)\). Using the condition \(a_n<400\), we get \(24+9(n-1)<400\), or \(n<42.78\). Hence, the greatest possible integer value is \(n=42\), so 42 terms are less than 400. For \(n=43\), the term is 402, which is not less than 400. Exam tip: For “less than” questions, retain the strict inequality \(<\) and select the greatest valid integer.