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The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
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Answer and explanation
Correct answer: -2
For an AP, the sixth term is \(a_6=a+5d\). Thus, \(23=a+5(5)=a+25\), so \(a=-2\). If the first term were 2, the sixth term would be \(2+25=27\), so that option is incorrect. Exam tip: in the \(n\)th-term formula, the coefficient of \(d\) is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
-2
Why is this the correct answer?
For an AP, the sixth term is \(a_6=a+5d\). Thus, \(23=a+5(5)=a+25\), so \(a=-2\). If the first term were 2, the sixth term would be \(2+25=27\), so that option is incorrect. Exam tip: in the \(n\)th-term formula, the coefficient of \(d\) is always \(n-1\).
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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