The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
Answer and explanation
Correct answer: 5
For an AP, the nth-term formula is \(a_n=a+(n-1)d\). Here, \(a=18\) and \(a_{16}=93\), so \(93=18+15d\). Thus, \(15d=75\), giving \(d=5\). If the common difference were 4, the 16th term would be \(18+15\times4=78\), not 93. Exam tip: use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
For an AP, the nth-term formula is \(a_n=a+(n-1)d\). Here, \(a=18\) and \(a_{16}=93\), so \(93=18+15d\). Thus, \(15d=75\), giving \(d=5\). If the common difference were 4, the 16th term would be \(18+15\times4=78\), not 93. Exam tip: use \(n-1\), not \(n\), in the nth-term formula.
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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