If (a_n=pn+q), (a_3=11), and (a_7=27), what will be (a_{12})?
Answer and explanation
Correct answer: 47
Given \(a_n=pn+q\), we have \(a_7-a_3=4p=27-11=16\), so \(p=4\). Using \(a_3=11\), \(12+q=11\), hence \(q=-1\). Therefore, \(a_{12}=4\times12-1=47\). Choosing 45 would correspond to \(4n-3\), which does not satisfy \(a_3=11\). Exam tip: when two terms are given, subtract them first to find \(p\).
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
Given \(a_n=pn+q\), we have \(a_7-a_3=4p=27-11=16\), so \(p=4\). Using \(a_3=11\), \(12+q=11\), hence \(q=-1\). Therefore, \(a_{12}=4\times12-1=47\). Choosing 45 would correspond to \(4n-3\), which does not satisfy \(a_3=11\). Exam tip: when two terms are given, subtract them first to find \(p\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
