What is the last term in the AP of positive multiples of (19) less than (1500)?
Answer and explanation
Correct answer: 1482
The positive multiples of 19 form the AP \(19, 38, 57, \ldots\). For the last term, \(19n<1500\). Since \(1500\div19\approx78.94\), the greatest integer value of \(n\) is 78. Thus, the last term is \(19\times78=1482\). Although \(1501=19\times79\), it is greater than 1500. Exam tip: for “less than,” take the integer part of the quotient and verify the multiple.
Frequently asked questions
What is the correct answer to this question?
1482
Why is this the correct answer?
The positive multiples of 19 form the AP \(19, 38, 57, \ldots\). For the last term, \(19n<1500\). Since \(1500\div19\approx78.94\), the greatest integer value of \(n\) is 78. Thus, the last term is \(19\times78=1482\). Although \(1501=19\times79\), it is greater than 1500. Exam tip: for “less than,” take the integer part of the quotient and verify the multiple.
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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