To solve the problem, we first analyze the sequence by examining the relationship between each term and its position (n):

Step 1: Identify the pattern

Let (a(n)) denote the (n)-th term. Observing the sequence:

• (n=1): (2 = 1^2 + 1^3 = 1^2(1+1))
• (n=2): (12 = 2^2 + 2^3 = 2^2(2+1))
• (n=3): (36 = 3^2 + 3^3 = 3^2(3+1))
• (n=4): (80 = 4^2 + 4^3 = 4^2(4+1))
• (n=5): (150 = 5^2 + 5^3 = 5^2(5+1))
• (n=6): (252 = 6^2 + 6^3 = 6^2(6+1))

Step 2: General formula

The pattern simplifies to:
(a(n) = n^2(n+1))

Step 3: Calculate the next term ((n=7))

(a(7) = 7^2(7+1) = 49 \times 8 = 392)

Answer: 392

作者声明:本文包含人工智能生成内容。