To determine the next number in the series 2, 3, 4, 8, 9, 10, 20, 21, 22, let’s first analyze the pattern of the series.
The series can be divided into two distinct groups:
- The first group consists of the numbers: 2, 4, 8, 20. These numbers can be derived by multiplying the previous number by 2, leading to 2, then doubling to get 4, doubling again for 8, and finally doubling 20 to get 40.
- The second group is simply consecutive numbers that follow after each doubling: 3 (after 2), 9 (after 8), 10 (after 9), 21 (after 20), and lastly 22 (after 21).
In this alternating pattern, after 22, we would investigate the next doubling pattern. The next number in this sequential part (after 22) should follow the last doubling pattern. Since 20 was followed by 21 and then 22, the next logical doubling in that consistent pattern after 20 is 40. Therefore, the next number in the series is:
40.