If the (12)th term of the AP (y,y+6,y+12,\ldots) is (89), what is the value of (y)?
Answer and explanation
Correct answer: \(23\)
For this AP, the first term is \(a=y\) and the common difference is \(d=6\). The 12th term is \(a_{12}=a+(12-1)d\). Therefore, \(89=y+11\times6=y+66\), so \(y=23\). If \(y=21\), the 12th term would be \(87\), not \(89\). Exam tip: use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(23\)
Why is this the correct answer?
For this AP, the first term is \(a=y\) and the common difference is \(d=6\). The 12th term is \(a_{12}=a+(12-1)d\). Therefore, \(89=y+11\times6=y+66\), so \(y=23\). If \(y=21\), the 12th term would be \(87\), not \(89\). 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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