Which is the nth term of the sequence 8, 21, 40, 65, 96, …?
Answer and explanation
Correct answer: 3n² + 4n + 1
The sequence has first differences 13, 19, 25, and 31; these increase by 6, so a quadratic formula is appropriate. Test option C at the first few indices: for n = 1, 3(1)² + 4(1) + 1 = 8; for n = 2, 3(4) + 8 + 1 = 21; for n = 3, 3(9) + 12 + 1 = 40. It also gives n = 4: 48 + 16 + 1 = 65, and n = 5: 75 + 20 + 1 = 96. Hence aₙ = 3n² + 4n + 1 and option C is correct. The other formulas fail at least one early term, so checking several indices removes accidental matches.
Frequently asked questions
What is the correct answer to this question?
3n² + 4n + 1
Why is this the correct answer?
The sequence has first differences 13, 19, 25, and 31; these increase by 6, so a quadratic formula is appropriate. Test option C at the first few indices: for n = 1, 3(1)² + 4(1) + 1 = 8; for n = 2, 3(4) + 8 + 1 = 21; for n = 3, 3(9) + 12 + 1 = 40. It also gives n = 4: 48 + 16 + 1 = 65, and n = 5: 75 + 20 + 1 = 96. Hence aₙ = 3n² + 4n + 1 and option C is correct. The other formulas fail at least one early term, so checking several indices removes accidental matches.
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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