The AP of multiples of (23) greater than (900) is (920,943,966,\ldots). What will be its (27)th term?
Answer and explanation
Correct answer: 1518
The first term is \(a=920\), and the common difference is \(d=943-920=23\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{27}=920+(27-1)\times23=920+598=1518\). The value 1541 results from incorrectly using \(n\) instead of \((n-1)\). Exam tip: there are always \(n-1\) common differences between the first term and the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
1518
Why is this the correct answer?
The first term is \(a=920\), and the common difference is \(d=943-920=23\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{27}=920+(27-1)\times23=920+598=1518\). The value 1541 results from incorrectly using \(n\) instead of \((n-1)\). Exam tip: there are always \(n-1\) common differences between the first term and 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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