In the AP (-12,-5,2,\ldots), what is the first term greater than (100)?
Answer and explanation
Correct answer: 107
Here, the first term is \(a=-12\) and the common difference is \(d=7\). Thus, \(a_n=-12+7(n-1)=7n-19\). For \(a_n>100\), we get \(7n-19>100\), so \(n>17\). The smallest integer value is \(n=18\), and \(a_{18}=107\). While 100 is the 17th term, the next AP term is 107. Exam tip: for “greater than,” solve the inequality and take the smallest valid integer value of \(n\).
Frequently asked questions
What is the correct answer to this question?
107
Why is this the correct answer?
Here, the first term is \(a=-12\) and the common difference is \(d=7\). Thus, \(a_n=-12+7(n-1)=7n-19\). For \(a_n>100\), we get \(7n-19>100\), so \(n>17\). The smallest integer value is \(n=18\), and \(a_{18}=107\). While 100 is the 17th term, the next AP term is 107. Exam tip: for “greater than,” solve the inequality and take the smallest 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.
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