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: Start from the known end of the sequence and work backward.
The last term is 8. Ask what simple operation could turn the 4th term into this 5th term. Since $2^3=8$, cubing a small whole number is a strong candidate.

Step 2: Test the same operation earlier in the sequence.
Check the 2nd and 3rd terms with the same idea: the 2nd term is 0, and cubing it gives $0^3=0$, which matches the 3rd term exactly. This confirms the rule: each term at an odd position is the cube of the even-positioned term just before it.

Step 3: Apply the confirmed rule to the missing spot.
The 4th term feeds into the 5th term through this same cubing rule, so the 4th term must be the cube root of 8, which is $\sqrt[3]{8}=2$.

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