What is the general term of the sequence 3, 16, 41, 78, …?
Answer and explanation
Correct answer: aₙ = 6n² − 5n + 2
The governing concept is finding an explicit general term from a sequence. The first differences are 13, 25, and 37; their second differences are both 12, indicating a quadratic rule. Test option A: for n = 1, 6 − 5 + 2 = 3; for n = 2, 24 − 10 + 2 = 16; for n = 3, 54 − 15 + 2 = 41; and for n = 4, 96 − 20 + 2 = 78. It matches every given term, so option A is correct. The linear option C cannot have changing first differences, and B and D fail on one or more terms.
Frequently asked questions
What is the correct answer to this question?
aₙ = 6n² − 5n + 2
Why is this the correct answer?
The governing concept is finding an explicit general term from a sequence. The first differences are 13, 25, and 37; their second differences are both 12, indicating a quadratic rule. Test option A: for n = 1, 6 − 5 + 2 = 3; for n = 2, 24 − 10 + 2 = 16; for n = 3, 54 − 15 + 2 = 41; and for n = 4, 96 − 20 + 2 = 78. It matches every given term, so option A is correct. The linear option C cannot have changing first differences, and B and D fail on one or more terms.
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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