What is the nth term of the sequence 1, 3, 7, 15, 31, …?
Answer and explanation
Correct answer: 2ⁿ − 1
The governing concept is an explicit or general rule for a sequence. Each listed term is one less than a power of 2: 1 = 2¹ − 1, 3 = 2² − 1, 7 = 2³ − 1, 15 = 2⁴ − 1, and 31 = 2⁵ − 1. Therefore, when the position is n, the corresponding power is 2ⁿ, so the nth term is aₙ = 2ⁿ − 1. Option A is correct. Option B would begin with 3 rather than 1, option C gives a linear sequence, and option D does not reproduce the given terms.
Frequently asked questions
What is the correct answer to this question?
2ⁿ − 1
Why is this the correct answer?
The governing concept is an explicit or general rule for a sequence. Each listed term is one less than a power of 2: 1 = 2¹ − 1, 3 = 2² − 1, 7 = 2³ − 1, 15 = 2⁴ − 1, and 31 = 2⁵ − 1. Therefore, when the position is n, the corresponding power is 2ⁿ, so the nth term is aₙ = 2ⁿ − 1. Option A is correct. Option B would begin with 3 rather than 1, option C gives a linear sequence, and option D does not reproduce the given terms.
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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