In an arithmetic sequence, (a_4=18) and the common difference is (5). What will be the explicit rule?
Answer and explanation
Correct answer: \(a_n=5n-2\)
For an arithmetic sequence, \(a_n=a_1+(n-1)d\). Here, \(a_4=a_1+3(5)=18\), so \(a_1=3\). Hence \(a_n=3+(n-1)5=5n-2\), making option A correct. In option B, \(a_4=22\), so it cannot be correct. Exam tip: when a term \(a_k\) is given, first find \(a_1=a_k-(k-1)d\), then form the general term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=5n-2\)
Why is this the correct answer?
For an arithmetic sequence, \(a_n=a_1+(n-1)d\). Here, \(a_4=a_1+3(5)=18\), so \(a_1=3\). Hence \(a_n=3+(n-1)5=5n-2\), making option A correct. In option B, \(a_4=22\), so it cannot be correct. Exam tip: when a term \(a_k\) is given, first find \(a_1=a_k-(k-1)d\), then form the general 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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