What is the nth term of the sequence 10, 18, 34, 66, 130, …?
Answer and explanation
Correct answer: 2ⁿ⁺² + 2
The sequence is not arithmetic because its successive differences are 8, 16, 32, and 64. Instead, each term can be written as a power of 2 plus 2: 10 = 2³ + 2, 18 = 2⁴ + 2, 34 = 2⁵ + 2, 66 = 2⁶ + 2, and 130 = 2⁷ + 2. The exponent is n + 2 when the first term corresponds to n = 1. Hence the general term is aₙ = 2ⁿ⁺² + 2, so option A is correct. Option B gives 10 for n = 1 but then gives 22 for n = 2, not 18. Option C gives 12 as the first term, and option D describes a linear pattern, which this sequence clearly is not.
Frequently asked questions
What is the correct answer to this question?
2ⁿ⁺² + 2
Why is this the correct answer?
The sequence is not arithmetic because its successive differences are 8, 16, 32, and 64. Instead, each term can be written as a power of 2 plus 2: 10 = 2³ + 2, 18 = 2⁴ + 2, 34 = 2⁵ + 2, 66 = 2⁶ + 2, and 130 = 2⁷ + 2. The exponent is n + 2 when the first term corresponds to n = 1. Hence the general term is aₙ = 2ⁿ⁺² + 2, so option A is correct. Option B gives 10 for n = 1 but then gives 22 for n = 2, not 18. Option C gives 12 as the first term, and option D describes a linear pattern, which this sequence clearly is not.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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