The AP of multiples of (13) greater than (250) is (260,273,286,\ldots). What is its (22)nd term?
Answer and explanation
Correct answer: 533
The first term of the AP is \(a=260\), and the common difference is \(d=273-260=13\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(a_{22}=260+(22-1)\times13=260+273=533\). Therefore, 533 is correct. The number 546 is the next, or 23rd, term. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
533
Why is this the correct answer?
The first term of the AP is \(a=260\), and the common difference is \(d=273-260=13\). The \(n\)th term is \(a_n=a+(n-1)d\). Thus, \(a_{22}=260+(22-1)\times13=260+273=533\). Therefore, 533 is correct. The number 546 is the next, or 23rd, term. Exam tip: use \(n-1\), not \(n\), in the formula for the \(n\)th term.
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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