What is the last term in the AP of positive multiples of (17) less than (1000)?
Answer and explanation
Correct answer: 986
The AP of positive multiples of 17 is \(17, 34, 51, \ldots\). Its last term has the form \(17n\), with \(17n<1000\). Since \(1000\div17\approx58.82\), the greatest integer value of \(n\) is 58. Therefore, the last term is \(17\times58=986\). Although \(1003=17\times59\), it is not less than 1000. Exam tip: For “less than” limits, take the integer part of the quotient and verify by multiplication.
Frequently asked questions
What is the correct answer to this question?
986
Why is this the correct answer?
The AP of positive multiples of 17 is \(17, 34, 51, \ldots\). Its last term has the form \(17n\), with \(17n<1000\). Since \(1000\div17\approx58.82\), the greatest integer value of \(n\) is 58. Therefore, the last term is \(17\times58=986\). Although \(1003=17\times59\), it is not less than 1000. Exam tip: For “less than” limits, take the integer part of the quotient and verify by multiplication.
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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