In the AP (8,14,20,\ldots), (a_n=74). Find the value of (n).
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Answer and explanation
Correct answer: 12
The first term is 8 and the common difference is 6. Using \(a_n=a+(n-1)d\), \(74=8+(n-1)\times6\). Thus, \(66=6(n-1)\), so \(n-1=11\) and \(n=12\). If \(n=13\), the term would be \(8+12\times6=80\), not 74. Exam tip: after finding \(n-1\), remember to add 1 to obtain the term number.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The first term is 8 and the common difference is 6. Using \(a_n=a+(n-1)d\), \(74=8+(n-1)\times6\). Thus, \(66=6(n-1)\), so \(n-1=11\) and \(n=12\). If \(n=13\), the term would be \(8+12\times6=80\), not 74. Exam tip: after finding \(n-1\), remember to add 1 to obtain the term number.
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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