If (a_n=an+b), (a_2+a_9=54), and (a_4+a_{11}=78), what will be (a_{12})?
Answer and explanation
Correct answer: \(66\)
Interpret the given linear term as \(a_n=an+b\). Then \(a_2+a_9=11a+2b=54\) and \(a_4+a_{11}=15a+2b=78\). Subtracting the first equation from the second gives \(4a=24\), so \(a=6\). Using \(11(6)+2b=54\), we get \(b=-6\). Hence, \(a_{12}=12(6)-6=66\). The nearby option \(63\) does not follow from this linear expression. Exam tip: subtract such pair-sum equations first to eliminate the constant term \(b\).
Frequently asked questions
What is the correct answer to this question?
\(66\)
Why is this the correct answer?
Interpret the given linear term as \(a_n=an+b\). Then \(a_2+a_9=11a+2b=54\) and \(a_4+a_{11}=15a+2b=78\). Subtracting the first equation from the second gives \(4a=24\), so \(a=6\). Using \(11(6)+2b=54\), we get \(b=-6\). Hence, \(a_{12}=12(6)-6=66\). The nearby option \(63\) does not follow from this linear expression. Exam tip: subtract such pair-sum equations first to eliminate the constant term \(b\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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