If aₙ = (n² + 1)/n, what is the value of a₄?
Answer and explanation
Correct answer: 17/4
The governing concept is evaluation of an explicit sequence rule at a specified index. The notation a₄ means that n must be replaced by 4 throughout the formula, not only in one part. Thus a₄ = (4² + 1)/4 = (16 + 1)/4 = 17/4. The fraction is already in simplest form because 17 is prime and is not divisible by 4. Option B would result from incorrectly using 4² − 1, while option C changes the numerator without justification. Option D, 9/2, is equal to 18/4, so it also does not follow from the substitution. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
17/4
Why is this the correct answer?
The governing concept is evaluation of an explicit sequence rule at a specified index. The notation a₄ means that n must be replaced by 4 throughout the formula, not only in one part. Thus a₄ = (4² + 1)/4 = (16 + 1)/4 = 17/4. The fraction is already in simplest form because 17 is prime and is not divisible by 4. Option B would result from incorrectly using 4² − 1, while option C changes the numerator without justification. Option D, 9/2, is equal to 18/4, so it also does not follow from the substitution. Therefore option A is correct.
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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