If \(a_n=\frac{3n-2}{2n+1}\), what is the value of \(a_7\)?
Answer and explanation
Correct answer: \(\frac{19}{15}\)
The governing idea is direct substitution into an explicit formula. Replace \(n\) by 7 in both the numerator and denominator: \(a_7=\frac{3(7)-2}{2(7)+1}=\frac{21-2}{14+1}=\frac{19}{15}\). Since 19 and 15 have no common factor, the fraction is already in simplest form. Therefore option C is correct. A common error is to compute the numerator correctly but use an incorrect denominator, producing options A, B, or D. The index must be substituted consistently in every occurrence of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{19}{15}\)
Why is this the correct answer?
The governing idea is direct substitution into an explicit formula. Replace \(n\) by 7 in both the numerator and denominator: \(a_7=\frac{3(7)-2}{2(7)+1}=\frac{21-2}{14+1}=\frac{19}{15}\). Since 19 and 15 have no common factor, the fraction is already in simplest form. Therefore option C is correct. A common error is to compute the numerator correctly but use an incorrect denominator, producing options A, B, or D. The index must be substituted consistently in every occurrence of \(n\).
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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