In the AP (20,31,42,\ldots), what is the greatest term between (500) and (600)?
Answer and explanation
Correct answer: 592
Here, the first term is 20 and the common difference is 11. Thus, \(a_n=20+11(n-1)=11n+9\). For a term below 600, \(11n+9<600\), so \(n<53.73\). Hence the greatest possible integer value is \(n=53\), giving \(a_{53}=11\times53+9=592\). The next term, 603, is greater than 600. Exam tip: In range questions, use an inequality first and then take the greatest valid integer value of n.
Frequently asked questions
What is the correct answer to this question?
592
Why is this the correct answer?
Here, the first term is 20 and the common difference is 11. Thus, \(a_n=20+11(n-1)=11n+9\). For a term below 600, \(11n+9<600\), so \(n<53.73\). Hence the greatest possible integer value is \(n=53\), giving \(a_{53}=11\times53+9=592\). The next term, 603, is greater than 600. Exam tip: In range questions, use an inequality first and then take the greatest valid integer value of n.
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.
