Which is the nth term of the sequence 4, 6, 10, 18, 34, …?
Answer and explanation
Correct answer: 2ⁿ + 2
The governing concept is identifying an explicit rule by separating the variable pattern from a constant. The terms can be rewritten as 2 + 2, 4 + 2, 8 + 2, 16 + 2, and 32 + 2. The powers are 2¹, 2², 2³, 2⁴, and 2⁵, so the nth term is aₙ = 2ⁿ + 2. Hence option A is correct. Direct checking gives a₁ = 2 + 2 = 4, a₂ = 4 + 2 = 6, and a₅ = 32 + 2 = 34. Option B gives 4 at n = 1, option C gives 4 at n = 1 but 8 at n = 2, and option D introduces an extra changing n instead of the constant addition.
Frequently asked questions
What is the correct answer to this question?
2ⁿ + 2
Why is this the correct answer?
The governing concept is identifying an explicit rule by separating the variable pattern from a constant. The terms can be rewritten as 2 + 2, 4 + 2, 8 + 2, 16 + 2, and 32 + 2. The powers are 2¹, 2², 2³, 2⁴, and 2⁵, so the nth term is aₙ = 2ⁿ + 2. Hence option A is correct. Direct checking gives a₁ = 2 + 2 = 4, a₂ = 4 + 2 = 6, and a₅ = 32 + 2 = 34. Option B gives 4 at n = 1, option C gives 4 at n = 1 but 8 at n = 2, and option D introduces an extra changing n instead of the constant addition.
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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