In the AP (42,55,68,\ldots), how many terms are less than (1000)?
Answer and explanation
Correct answer: 74
Here, the first term is \(a=42\) and the common difference is \(d=13\). The \(n\)th term is \(a_n=42+13(n-1)\). From \(42+13(n-1)<1000\), we get \(13n<971\), so \(n<74.69\). Hence, there are \(74\) terms less than 1000. The \(75\)th term is \(1017\), which is not less than 1000. Exam tip: after solving an inequality for the number of terms, take the greatest integer satisfying it.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
Here, the first term is \(a=42\) and the common difference is \(d=13\). The \(n\)th term is \(a_n=42+13(n-1)\). From \(42+13(n-1)<1000\), we get \(13n<971\), so \(n<74.69\). Hence, there are \(74\) terms less than 1000. The \(75\)th term is \(1017\), which is not less than 1000. Exam tip: after solving an inequality for the number of terms, take the greatest integer satisfying it.
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.
