If a_n = 4n² − 1, which term is 575?
Answer and explanation
Correct answer: 12th
The governing concept is finding a term position from an nth-term formula. We seek n such that 4n² − 1 = 575. Adding 1 to both sides gives 4n² = 576. Dividing by 4 gives n² = 144, so the positive term position is n = 12; a sequence position cannot be negative. Direct substitution confirms this: a_12 = 4(12²) − 1 = 4 × 144 − 1 = 576 − 1 = 575. Therefore option C is correct. The nearby choices give a_11 = 483 and a_13 = 675, so they cannot produce 575. The negative square root is rejected because term numbers are positive integers.
Frequently asked questions
What is the correct answer to this question?
12th
Why is this the correct answer?
The governing concept is finding a term position from an nth-term formula. We seek n such that 4n² − 1 = 575. Adding 1 to both sides gives 4n² = 576. Dividing by 4 gives n² = 144, so the positive term position is n = 12; a sequence position cannot be negative. Direct substitution confirms this: a_12 = 4(12²) − 1 = 4 × 144 − 1 = 576 − 1 = 575. Therefore option C is correct. The nearby choices give a_11 = 483 and a_13 = 675, so they cannot produce 575. The negative square root is rejected because term numbers are positive integers.
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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