Identify Number Sequence Pattern

The question presents a number sequence: 1, 8, 27, 64, 125, ?, 343.

We need to find the missing number represented by the question mark.

Analyze the Sequence Terms

Let's examine the relationship between the numbers in the sequence:

• The first term is 1, which is $1^3$ (1 x 1 x 1).
• The second term is 8, which is $2^3$ (2 x 2 x 2).
• The third term is 27, which is $3^3$ (3 x 3 x 3).
• The fourth term is 64, which is $4^3$ (4 x 4 x 4).
• The fifth term is 125, which is $5^3$ (5 x 5 x 5).
• The seventh term is 343, which is $7^3$ (7 x 7 x 7).

Determine the Missing Term's Position

The sequence follows the pattern of cubes of consecutive positive integers ($n^3$). The terms correspond to $n=1, 2, 3, 4, 5, ?, 7$.

The missing term is in the 6th position, so it should correspond to $n=6$.

Calculate the Missing Number

To find the missing number, we calculate the cube of 6:

$ 6^3 = 6 \times 6 \times 6 = 216 $

Therefore, the missing number in the sequence is 216.