What is the next number in the sequence $7,10,16,28$?

• A. $52$
• B. $40$
• C. $56$
• D. $44$

Answer: (A)

Verified step by step guidance

1. First, observe the given sequence: 7, 10, 16, 28. To find the next number, start by calculating the differences between consecutive terms.
2. Calculate the first differences: 10 - 7 = 3, 16 - 10 = 6, and 28 - 16 = 12. Write these differences as a new sequence: 3, 6, 12.
3. Next, examine the pattern in the first differences. Calculate the second differences: 6 - 3 = 3 and 12 - 6 = 6. Write these as a new sequence: 3, 6.
4. Look for a pattern in the second differences. Since they are increasing, consider if the differences are doubling or following a specific pattern. Predict the next second difference based on this pattern.
5. Use the predicted second difference to find the next first difference by adding it to the last first difference. Then, add this new first difference to the last term in the original sequence to find the next number.