List the first four terms of each sequence whose general term is given.
(B) $a_n=n^2-4n+2$

• A. $-1,-2,-1,2$
• B. $2,-1,-2,-1$
• C. $0,-1,-2,-1$
• D. $-2,-1,2,7$

Answer: (A)

Verified step by step guidance

1. Since the problem is about sequences, start by identifying the type of sequence you are dealing with. Common types include arithmetic sequences (where each term increases by a constant difference) and geometric sequences (where each term is multiplied by a constant ratio).
2. If the sequence is arithmetic, use the formula for the nth term: \(a_n = a_1 + (n - 1) \times d\), where \(a_1\) is the first term and \(d\) is the common difference.
3. If the sequence is geometric, use the formula for the nth term: \(a_n = a_1 \times r^{n-1}\), where \(a_1\) is the first term and \(r\) is the common ratio.
4. To find a specific term, substitute the known values (first term, common difference or ratio, and the term number) into the appropriate formula.
5. If the problem asks for the sum of terms, use the sum formulas: for arithmetic sequences, \(S_n = \frac{n}{2} (2a_1 + (n-1)d)\); for geometric sequences, \(S_n = a_1 \times \frac{1 - r^n}{1 - r}\) (when \(r \neq 1\)).