If \(a_6=2a_3+5\) and \(a_3=13\), what is \(a_{12}\)?
Answer and explanation
Correct answer: 67
Given \(a_3=13\), \(a_6=2(13)+5=31\). In an AP, \(a_6-a_3=(6-3)d=3d\). Hence, \(31-13=18=3d\), so \(d=6\). Now \(a_{12}=a_3+(12-3)d=13+9\times6=67\). Therefore, 67 is correct. A value such as 69 can result from incorrectly counting the number of common differences. Exam tip: when using \(a_n=a_r+(n-r)d\), carefully use \(n-r\) as the number of gaps.
Frequently asked questions
What is the correct answer to this question?
67
Why is this the correct answer?
Given \(a_3=13\), \(a_6=2(13)+5=31\). In an AP, \(a_6-a_3=(6-3)d=3d\). Hence, \(31-13=18=3d\), so \(d=6\). Now \(a_{12}=a_3+(12-3)d=13+9\times6=67\). Therefore, 67 is correct. A value such as 69 can result from incorrectly counting the number of common differences. Exam tip: when using \(a_n=a_r+(n-r)d\), carefully use \(n-r\) as the number of gaps.
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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