Which general term is correct for the sequence (2, 9, 21, 38, …)?
Answer and explanation
Correct answer: aₙ = n(5n − 1)/2
The governing concept is an explicit or general rule: one formula must produce the term for every positive integer n. Test option A by substituting n = 1, 2, 3 and 4: a₁ = 1(5−1)/2 = 2, a₂ = 2(10−1)/2 = 9, a₃ = 3(15−1)/2 = 21, and a₄ = 4(20−1)/2 = 38. Therefore option A reproduces all given terms. Option B gives 3, 7, 12, 18, while option C gives 2, 9, 16, 23 and option D gives 2, 8, 18, 32, so those distractors fail the direct substitution check.
Frequently asked questions
What is the correct answer to this question?
aₙ = n(5n − 1)/2
Why is this the correct answer?
The governing concept is an explicit or general rule: one formula must produce the term for every positive integer n. Test option A by substituting n = 1, 2, 3 and 4: a₁ = 1(5−1)/2 = 2, a₂ = 2(10−1)/2 = 9, a₃ = 3(15−1)/2 = 21, and a₄ = 4(20−1)/2 = 38. Therefore option A reproduces all given terms. Option B gives 3, 7, 12, 18, while option C gives 2, 9, 16, 23 and option D gives 2, 8, 18, 32, so those distractors fail the direct substitution check.
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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