To solve the problem, we first identify the pattern across the rows relative to the first row (which is (1,2,3,4)):

Step 1: Analyze the second row

The second row elements follow the formula:
(n^2 + 1) (where (n) is the corresponding element in the first row).

• (1^2 +1 =2), (2^2 +1=5), (3^2 +1=10), (4^2 +1=17) → matches the second row.

Step 2: Analyze the third row

The third row elements follow the formula:
(n^3 +2) (where (n) is the corresponding element in the first row).

• (1^3 +2=3), (2^3 +2=10), (3^3 +2=29) → matches the third row so far.

Step 3: Calculate the missing element

For the 4th element in the third row:
(4^3 +2 =64 +2=66).

Answer: (\boxed{66})

作者声明:本文包含人工智能生成内容。