To find the 10th term of the arithmetic sequence where the sum of the first (n) terms is (S_n = 3n^2 + 2n), follow these steps:

Step 1: Recall the relationship between (S_n) and the (n)-th term (a_n)

The (n)-th term of a sequence is given by:
(a_n = Sn - S{n-1})

Step 2: Compute (S_{n-1})

(S{n-1} = 3(n-1)^2 + 2(n-1))
Expand:
(S{n-1} = 3(n^2 - 2n + 1) + 2n - 2 = 3n^2 - 6n + 3 + 2n - 2 = 3n^2 - 4n + 1)

Step 3: Calculate (a_n)

(a_n = Sn - S{n-1} = (3n^2 + 2n) - (3n^2 - 4n + 1) = 6n - 1)

Step 4: Find the 10th term

(a_{10} = 6(10) - 1 = 59)

Answer: (\boxed{59})

作者声明:本文包含人工智能生成内容。