If \(a_n=\frac{2n^2+5n}{3}\), what is the value of \(a_6\)?
Answer and explanation
Correct answer: 34
Substitute \(n=6\): \(a_6=\frac{2(6)^2+5(6)}{3}=\frac{2\times36+30}{3}=\frac{72+30}{3}=\frac{102}{3}=34\). Hence, 34 is the correct option. An answer such as 36 can result from not dividing the complete numerator correctly by 3. Exam tip: substitute the value of \(n\) first, then follow the order of operations—powers, multiplication, addition, and finally division.
Frequently asked questions
What is the correct answer to this question?
34
Why is this the correct answer?
Substitute \(n=6\): \(a_6=\frac{2(6)^2+5(6)}{3}=\frac{2\times36+30}{3}=\frac{72+30}{3}=\frac{102}{3}=34\). Hence, 34 is the correct option. An answer such as 36 can result from not dividing the complete numerator correctly by 3. Exam tip: substitute the value of \(n\) first, then follow the order of operations—powers, multiplication, addition, and finally division.
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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