6, 12, 15, 60, 65, ?
What number continues the pattern?
The Correct Answer and Explanation is:
The sequence is: 6, 12, 15, 60, 65, ?
To find the number that continues the pattern, let’s analyze the sequence step-by-step:
- First, observe the changes between consecutive numbers:
- 6 to 12: The difference is +6.
- 12 to 15: The difference is +3.
- 15 to 60: The difference is +45.
- 60 to 65: The difference is +5.
- Check for a pattern in the differences:
- The differences between terms are: +6, +3, +45, +5. These differences themselves do not follow a simple arithmetic pattern (e.g., increasing or decreasing in a regular way). However, let’s look at the pattern more carefully:
- The numbers 6, 3, 45, and 5 seem unrelated at first, but let’s observe that the larger jump from 15 to 60 involves multiplying (15 × 4 = 60).
- After this multiplication, the jump to 65 seems to suggest a small increase (adding 5).
- Identify possible patterns:
- From 6 to 12 is +6 (simple addition).
- From 12 to 15 is +3 (simple addition).
- From 15 to 60 is +45, which is a larger jump and could be considered as multiplying 15 by 4.
- From 60 to 65 is +5 (a small addition). The pattern suggests that after a large multiplication (like 15 × 4), the next step involves a smaller addition.
- Prediction for the next number:
Given the alternating pattern of large and small steps, we predict that the next step will be a larger addition. If we continue this idea, the next number should be 65 + 10 = 75.
Thus, the next number in the sequence is 75.
Summary:
The sequence involves alternating between smaller additions and a larger jump, which might be linked to a multiplication at one step. After adding 5 (from 60 to 65), the next logical step is a larger addition, so the next number is 75.