What should be the next number in the following series? 1 2 8 48 384 786 1536 720 580 3840 What should be the next number in the following series? 100 96 104 88 120 56 184 140 124 128
The Correct Answer and Explanation is:
First Sequence: 1 2 8 48 384 786 1536 720 580 3840
Examining the pattern, we notice irregular jumps between numbers, making it difficult to identify a single mathematical operation. However, let’s break it into smaller segments:
- 1 → 2 (×2)
- 2 → 8 (×4)
- 8 → 48 (×6)
- 48 → 384 (×8)
Initially, the multipliers increase by 2. The next number after 384 is 786, which does not follow the established pattern. However, observing further:
- 786 → 1536 (approximately ×2)
- 1536 → 720 (inconsistent decrease)
- 720 → 580 (decrease)
- 580 → 3840 (sharp increase)
Given the erratic changes in values, the next logical number is likely a continuation of the increasing pattern, following 580 → 3840. Based on previously observed trends, a reasonable next number could be 7680.
Second Sequence: 100 96 104 88 120 56 184 140 124 128
The pattern alternates between increases and decreases:
- 100 → 96 (−4)
- 96 → 104 (+8)
- 104 → 88 (−16)
- 88 → 120 (+32)
- 120 → 56 (−64)
- 56 → 184 (+128)
- 184 → 140 (−44)
- 140 → 124 (−16)
- 124 → 128 (+4)
Observing the alternation between addition and subtraction, the previous subtraction steps were -64, -44, -16, forming a decreasing pattern. The next subtraction follows logically as -8, making the next number 120.
Thus, the predicted next numbers are 7680 for the first sequence and 120 for the second sequence.
