Write the first 4 terms of the sequence $a_{n}=n^2\(\cdot\]\left\)(n-1\(\right\))!$

• A. {1, 4, 18, 96}
• B. {1, 2, 6, 24}
• C. {0, 4, 18, 96}
• D. {0, 2, 6, 24}

Answer: (A)

Verified step by step guidance

1. Identify the formula for the sequence: a_n = n^2 \(\cdot\) (n-1)!
2. Calculate the first term by substituting n = 1 into the formula: a_1 = 1^2 \(\cdot\) (1-1)! = 1^2 \(\cdot\) 0! = 1 \(\cdot\) 1 = 1
3. Calculate the second term by substituting n = 2 into the formula: a_2 = 2^2 \(\cdot\) (2-1)! = 4 \(\cdot\) 1! = 4 \(\cdot\) 1 = 4
4. Calculate the third term by substituting n = 3 into the formula: a_3 = 3^2 \(\cdot\) (3-1)! = 9 \(\cdot\) 2! = 9 \(\cdot\) 2 = 18
5. Calculate the fourth term by substituting n = 4 into the formula: a_4 = 4^2 \(\cdot\) (4-1)! = 16 \(\cdot\) 3! = 16 \(\cdot\) 6 = 96