If (a_3=14) and (a_8=39) in an arithmetic sequence, what is the general term (a_n)?
Answer and explanation
Correct answer: \(5n-1\)
The common difference is \(d=\frac{a_8-a_3}{8-3}=\frac{39-14}{5}=5\). Hence, \(a_n=a_3+(n-3)d=14+5(n-3)=5n-1\). Therefore, \(5n-1\) is correct. Although \(4n+2\) gives \(a_3=14\), it gives \(a_8=34\), not 39. Exam tip: First find \(d=\frac{a_q-a_p}{q-p}\) from two known terms, then substitute either known term.
Frequently asked questions
What is the correct answer to this question?
\(5n-1\)
Why is this the correct answer?
The common difference is \(d=\frac{a_8-a_3}{8-3}=\frac{39-14}{5}=5\). Hence, \(a_n=a_3+(n-3)d=14+5(n-3)=5n-1\). Therefore, \(5n-1\) is correct. Although \(4n+2\) gives \(a_3=14\), it gives \(a_8=34\), not 39. Exam tip: First find \(d=\frac{a_q-a_p}{q-p}\) from two known terms, then substitute either known term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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