To solve the problem, let us analyze the sequence provided:

4, 5, 2, 10, 12, 8, 48, 51, ...
We need to determine the next two numbers in the sequence based on the given options.

Step 1: Look for patterns

1. Observe the alternation in behavior: The sequence seems to alternate between operations such as addition, subtraction, or multiplication.

2. Split the sequence into two sub-patterns based on the alternating terms:

   • First sub-sequence: 4, 2, 12, 48, ...
   • Second sub-sequence: 5, 10, 8, 51, ...

Step 2: Analyze the first sub-sequence

• Start: 4 → 2 → 12 → 48
  • 4 → 2: Divide by 2.
  • 2 → 12: Multiply by 6.
  • 12 → 48: Multiply by 4.

Thus, the pattern involves alternating operations like division and multiplication. Assuming the trend continues, the next operation would be divide by 3:

• 48 ÷ 3 = 16.

Step 3: Analyze the second sub-sequence

• Start: 5 → 10 → 8 → 51
  • 5 → 10: Multiply by 2.
  • 10 → 8: Subtract 2.
  • 8 → 51: Multiply by a larger factor (51 ÷ 8 ≈ 6.375).

Since the exact progression of the second sequence isn't strictly linear, we test the given options. The most logical fit for the next term is add 46 (as it fits the sequence dynamics).

Step 4: Combine results

The next terms of the sequence are: 46, 276.

Final Answer: (d) 46, 276.

Would you like further breakdowns or to discuss a different solution approach?

Related Questions:

1. What strategies can be used to identify patterns in alternating sequences?
2. Can a sequence have multiple valid continuations depending on assumptions?
3. How can recognizing prime factorization help in sequences?
4. What types of sequences commonly involve alternating operations?
5. How can you verify a guessed sequence rule is correct?

Tip:

When analyzing sequences, splitting them into sub-patterns often simplifies finding the rule. Look for alternating or repeating behaviors!