In the AP (24,33,42,\ldots), how many terms are less than (400)?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
