Explanation:

Let's break down the sequence: 1, 5, 9, ?, 21

- First, look for the pattern in the differences:

- 5 - 1 = 4

- 9 - 5 = 4

- So, the pattern adds 4 to the previous term.

- Continue the pattern:

- 9 + 4 = 13 (so ? = 13)

- 13 + 8 = 21 (but this jump is 8, not 4, indicating there might be a different pattern or a mistake in the sequence logic)

Now let's check the given options:

- Option 1: 20 — Does not fit (difference from 9 is 11, and from 20 to 21 is 1).

- Option 2: 11 — Difference is 2, which breaks the pattern.

- Option 3: 19 — Difference is 10 (doesn't fit the previous pattern).

- Option 4: 15 — 9 to 15 is 6, 15 to 21 is 6 (so perhaps the pattern alternates: 4, 4, 6, 6).

So, let's review the pattern:

- 1 to 5: +4

- 5 to 9: +4

- 9 to 15: +6

- 15 to 21: +6

Option 4: 15 matches this new pattern.

- Option 4: 15 (Correct — continues the alternating pattern of adding 4, then 6).