What is the general term of the sequence 2, 12, 26, 44, …?
Answer and explanation
Correct answer: aₙ = 3n² + n − 2
The governing concept is selecting a quadratic general rule by using finite differences. The first differences are 12−2 = 10, 26−12 = 14, and 44−26 = 18. Their differences are 4 and 4, so a quadratic rule is appropriate. Test option A: for n = 1, 3(1)² + 1 − 2 = 2; for n = 2, 3(2)² + 2 − 2 = 12; for n = 3, 27 + 3 − 2 = 28, not 26. Thus the supplied key is wrong. Option B gives 6, 12, 22, 36; C gives 2, 12, 22, 32; and D gives 2, 14, 28, 44. None matches all four terms, so the item needs correction.
Frequently asked questions
What is the correct answer to this question?
aₙ = 3n² + n − 2
Why is this the correct answer?
The governing concept is selecting a quadratic general rule by using finite differences. The first differences are 12−2 = 10, 26−12 = 14, and 44−26 = 18. Their differences are 4 and 4, so a quadratic rule is appropriate. Test option A: for n = 1, 3(1)² + 1 − 2 = 2; for n = 2, 3(2)² + 2 − 2 = 12; for n = 3, 27 + 3 − 2 = 28, not 26. Thus the supplied key is wrong. Option B gives 6, 12, 22, 36; C gives 2, 12, 22, 32; and D gives 2, 14, 28, 44. None matches all four terms, so the item needs correction.
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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