In an arithmetic sequence, (a_4=18) and (a_9=43). What is the formula for (a_n)?
Answer and explanation
Correct answer: \(5n-2\)
For an arithmetic sequence, \(a_n=a_1+(n-1)d\). The difference between the given terms is \(a_9-a_4=43-18=25\), while the difference between their positions is \(9-4=5\). Hence, \(d=25/5=5\). Using \(a_4=a_1+3d\), we get \(18=a_1+15\), so \(a_1=3\). Therefore, \(a_n=3+(n-1)5=5n-2\). Option \(5n+2\) gives 22 when \(n=4\), so it is incorrect. Exam tip: when two terms are given, first find \(d\) by dividing the difference of the terms by the difference of their indices.
Frequently asked questions
What is the correct answer to this question?
\(5n-2\)
Why is this the correct answer?
For an arithmetic sequence, \(a_n=a_1+(n-1)d\). The difference between the given terms is \(a_9-a_4=43-18=25\), while the difference between their positions is \(9-4=5\). Hence, \(d=25/5=5\). Using \(a_4=a_1+3d\), we get \(18=a_1+15\), so \(a_1=3\). Therefore, \(a_n=3+(n-1)5=5n-2\). Option \(5n+2\) gives 22 when \(n=4\), so it is incorrect. Exam tip: when two terms are given, first find \(d\) by dividing the difference of the terms by the difference of their indices.
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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