Which explicit rule is correct for the sequence 11, 18, 32, 60, …?
Answer and explanation
Correct answer: aₙ = 7·2ⁿ⁻¹ + 4
An explicit rule must generate each term from n without needing the preceding term. Test option A: at n = 1, it gives 7·2⁰ + 4 = 11; at n = 2, it gives 7·2¹ + 4 = 18; at n = 3, it gives 7·2² + 4 = 32; and at n = 4, it gives 7·2³ + 4 = 60. Therefore A exactly matches the sequence. Option B gives 11, 22, 33, 44 and is not the sequence. Option C begins 11 but gives 13 at n = 2, while option D gives 11 at n = 1 but 23 at n = 2. Matching several positions, rather than only the first term, establishes the answer.
Frequently asked questions
What is the correct answer to this question?
aₙ = 7·2ⁿ⁻¹ + 4
Why is this the correct answer?
An explicit rule must generate each term from n without needing the preceding term. Test option A: at n = 1, it gives 7·2⁰ + 4 = 11; at n = 2, it gives 7·2¹ + 4 = 18; at n = 3, it gives 7·2² + 4 = 32; and at n = 4, it gives 7·2³ + 4 = 60. Therefore A exactly matches the sequence. Option B gives 11, 22, 33, 44 and is not the sequence. Option C begins 11 but gives 13 at n = 2, while option D gives 11 at n = 1 but 23 at n = 2. Matching several positions, rather than only the first term, establishes the answer.
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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