If \(a_{n+2}-a_n=18\) and \(a_9=74\), what is \(a_{25}\)?
Answer and explanation
Correct answer: 218
In an AP, \(a_{n+2}-a_n=2d\). Thus, \(2d=18\), so \(d=9\). The 25th term is 16 positions after the 9th term; hence \(a_{25}=a_9+16d=74+16\times9=218\). Option 216 is not possible because its difference from 74 is 142, which is not a multiple of 9. Exam tip: subtract the term indices and multiply the result by the common difference.
Frequently asked questions
What is the correct answer to this question?
218
Why is this the correct answer?
In an AP, \(a_{n+2}-a_n=2d\). Thus, \(2d=18\), so \(d=9\). The 25th term is 16 positions after the 9th term; hence \(a_{25}=a_9+16d=74+16\times9=218\). Option 216 is not possible because its difference from 74 is 142, which is not a multiple of 9. Exam tip: subtract the term indices and multiply the result by the common difference.
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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