If (a_n=n^2+4n), for which (n) will (a_n=77)?
Answer and explanation
Correct answer: 7
Given n² + 4n = 77, we get n² + 4n − 77 = 0, or (n − 7)(n + 11) = 0. Thus, n = 7 or n = −11. Since a sequence index must be a positive integer, n = 7 is valid. Although −11 is an algebraic root, it cannot represent a term position. Exam tip: after solving, always check whether the value is an allowed sequence index.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
Given n² + 4n = 77, we get n² + 4n − 77 = 0, or (n − 7)(n + 11) = 0. Thus, n = 7 or n = −11. Since a sequence index must be a positive integer, n = 7 is valid. Although −11 is an algebraic root, it cannot represent a term position. Exam tip: after solving, always check whether the value is an allowed sequence index.
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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