Question

Find the missing number: -1, 0, 0, ____, 8

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Compare the 2nd and 3rd terms first: notice the 3rd is the cube of the 2nd, then use the same rule between the 4th and 5th terms.

Answer 1

The Correct Option is B

Step 1: Look at the 2nd and 3rd terms and see how they connect.
The 2nd term is 0 and the 3rd term is also 0. Notice that \( 0^3 = 0 \), so the 3rd term is exactly the cube of the 2nd term.

Step 2: Check if the same rule links the 4th and 5th terms.
If the pattern is that every term at an odd position equals the cube of the term right before it, then the 5th term should equal the cube of the 4th term. We are told the 5th term is 8.

Step 3: Solve for the missing 4th term.
We need a number whose cube is 8. Since \( 2^3 = 8 \), the 4th term must be 2.

Step 4: Sanity check the whole sequence.
With the 4th term as 2, the sequence reads -1, 0, 0, 2, 8. The 3rd term (0) is the cube of the 2nd term (0), and the 5th term (8) is the cube of the 4th term (2), so the same rule works cleanly in both places.

Final Answer:
The missing number is 2. \[ \boxed{2} \]