Which option gives the first four terms of aₙ = 2n(n + 1)?
Answer and explanation
Correct answer: 4, 12, 24, 40
The governing concept is substitution in an explicit or general rule. The rule gives each term directly from its position n, so use n = 1, 2, 3, and 4 in order. For n = 1, a₁ = 2(1)(1 + 1) = 4; for n = 2, a₂ = 2(2)(3) = 12; for n = 3, a₃ = 2(3)(4) = 24; and for n = 4, a₄ = 2(4)(5) = 40. Therefore option B is correct. Option A begins with values obtained from a different expression, while options C and D also shift the substitution and do not satisfy the given rule.
Frequently asked questions
What is the correct answer to this question?
4, 12, 24, 40
Why is this the correct answer?
The governing concept is substitution in an explicit or general rule. The rule gives each term directly from its position n, so use n = 1, 2, 3, and 4 in order. For n = 1, a₁ = 2(1)(1 + 1) = 4; for n = 2, a₂ = 2(2)(3) = 12; for n = 3, a₃ = 2(3)(4) = 24; and for n = 4, a₄ = 2(4)(5) = 40. Therefore option B is correct. Option A begins with values obtained from a different expression, while options C and D also shift the substitution and do not satisfy the given rule.
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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