Find the next number in the series: 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20, ...

Introduction / Context:
This is a number series question where you must identify the underlying pattern that generates the given sequence. Unlike simple arithmetic or geometric progressions, the series 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20, ... uses blocks of consecutive numbers separated by gaps. The challenge is to recognise how the blocks and the gaps are growing and then extend the pattern to find the next term.

Given Data / Assumptions:

• The series is: 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 20, ...
• We are asked to find the next number after 20.
• The pattern may involve groups of consecutive numbers combined with skipped intervals.

Concept / Approach:
Group the numbers into blocks of consecutive integers and observe the sizes of those blocks and the gaps in between. The first block is 2, 3, 4 (three consecutive numbers). Then there is a gap of three numbers 5, 6, 7 which do not appear. The next block is 8, 9, 10, 11 (four consecutive numbers), followed by a gap 12, 13, 14, 15 of four missing numbers. Then we see a block of five consecutive numbers: 16, 17, 18, 19, 20. This pattern suggests that each time, the series skips k numbers and then includes k + 1 consecutive numbers, where k increases as we move forward.

Step-by-Step Solution:
First block: 2, 3, 4 (three consecutive numbers). Numbers 5, 6, 7 are skipped (a gap of three numbers). Second block: 8, 9, 10, 11 (four consecutive numbers). Numbers 12, 13, 14, 15 are skipped (a gap of four numbers). Third block: 16, 17, 18, 19, 20 (five consecutive numbers). By continuing the pattern, after a block of five numbers, the next gap should contain five numbers: 21, 22, 23, 24, 25 are skipped. The next block must therefore be six consecutive numbers starting from 26. Thus, the next term after 20 is 26.

Verification / Alternative check:
We can verify the logic by writing the structure explicitly: skip 3, write 3; skip 4, write 4; skip 5, write 5; and so on. The observed data matches skip 3 (5 to 7) and write 3 (2 to 4), then skip 4 (12 to 15) and write 4 (8 to 11), then write 5 (16 to 20). Following this systematic pattern, the next operation must be skip 5 (21 to 25) and write 6 (26 to 31). The first number of that new block is clearly 26, confirming the answer.

Why Other Options Are Wrong:

• 27, 24, 25 and 30: These are numbers close to 26, but they do not respect the rule that the next visible number must start immediately after skipping 21 to 25.
• 27 would be the second number in the next block, not the first.

Common Pitfalls:
Many learners first attempt to look for a simple difference pattern between successive terms, which quickly breaks down in this sequence. Others try to link the series to squares or primes without success. When a series feels irregular, it often helps to group numbers into segments and look for regularity in group lengths or gaps. Drawing a number line and marking present and missing numbers also makes the pattern more visible.

Final Answer:
The next number in the series is 26.