Which is the correct rule for the sequence (2,7,14,23,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+2n-1\)
Taking the term number as \(n=1,2,3,\ldots\), the rule \(a_n=n^2+2n-1\) gives \(a_1=2\), \(a_2=7\), \(a_3=14\), and \(a_4=23\). Hence, option A is correct. The closest distractor, \(n^2+n\), gives the second term as \(6\), not \(7\). Exam tip: when first differences increase regularly, such as \(5,7,9\), test a quadratic rule.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+2n-1\)
Why is this the correct answer?
Taking the term number as \(n=1,2,3,\ldots\), the rule \(a_n=n^2+2n-1\) gives \(a_1=2\), \(a_2=7\), \(a_3=14\), and \(a_4=23\). Hence, option A is correct. The closest distractor, \(n^2+n\), gives the second term as \(6\), not \(7\). Exam tip: when first differences increase regularly, such as \(5,7,9\), test a quadratic rule.
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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