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The (12)th term of an AP is (71) and the common difference is (5). What is the first term?
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Answer and explanation
Correct answer: 16
For an AP, \(a_n=a+(n-1)d\). Thus, \(71=a+11\times5\), so \(a=71-55=16\). If 18 were taken as the first term, the 12th term would be \(18+11\times5=73\), not 71. Exam tip: use \((n-1)\), not \(n\), in the formula for the nth term.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
For an AP, \(a_n=a+(n-1)d\). Thus, \(71=a+11\times5\), so \(a=71-55=16\). If 18 were taken as the first term, the 12th term would be \(18+11\times5=73\), not 71. Exam tip: use \((n-1)\), not \(n\), in the formula for the nth 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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