What is the nth term of the sequence \(4,-7,10,-13,16,\ldots\)?
Answer and explanation
Correct answer: \((-1)^{n+1}(3n+1)\)
The absolute values are 4, 7, 10, 13, 16, which follow the linear pattern \(3n+1\): for \(n=1\), it gives 4, and each next value increases by 3. The signs alternate, beginning with positive. The factor \((-1)^{n+1}\) is positive when \(n=1\), negative when \(n=2\), and continues this alternating pattern. Hence the nth term is \((-1)^{n+1}(3n+1)\), so option A is correct. Option B starts with a negative first term, C omits alternating signs, and D has the wrong magnitude pattern.
Frequently asked questions
What is the correct answer to this question?
\((-1)^{n+1}(3n+1)\)
Why is this the correct answer?
The absolute values are 4, 7, 10, 13, 16, which follow the linear pattern \(3n+1\): for \(n=1\), it gives 4, and each next value increases by 3. The signs alternate, beginning with positive. The factor \((-1)^{n+1}\) is positive when \(n=1\), negative when \(n=2\), and continues this alternating pattern. Hence the nth term is \((-1)^{n+1}(3n+1)\), so option A is correct. Option B starts with a negative first term, C omits alternating signs, and D has the wrong magnitude pattern.
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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