In the AP (35,46,57,\ldots), how many terms are less than (600)?
Answer and explanation
Correct answer: 52
Here, the first term is \(a=35\) and the common difference is \(d=11\). The \(n\)th term is \(a_n=35+11(n-1)\). Using \(35+11(n-1)<600\), we get \(n<52.36\ldots\), so the greatest possible integer value is \(n=52\). Check: \(a_{52}=596<600\), whereas \(a_{53}=607>600\). Therefore, 52 terms are less than 600. Exam tip: For a ‘less than’ condition, verify the next term to confirm the count.
Frequently asked questions
What is the correct answer to this question?
52
Why is this the correct answer?
Here, the first term is \(a=35\) and the common difference is \(d=11\). The \(n\)th term is \(a_n=35+11(n-1)\). Using \(35+11(n-1)<600\), we get \(n<52.36\ldots\), so the greatest possible integer value is \(n=52\). Check: \(a_{52}=596<600\), whereas \(a_{53}=607>600\). Therefore, 52 terms are less than 600. Exam tip: For a ‘less than’ condition, verify the next term to confirm the count.
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.
