Decreasing number patterns, step by step

A shrinking sequence hides a rule just as a growing one does — it takes a fixed amount away each time.

The question

11, ?, 7, 5, 3

11?753
11?753
11?753
11?753
119753
  1. Find the rule first, from two numbers you can actually see — never from the gap.
  2. 7 to 5 is − 2. One pair is a guess, though — check it against another.
  3. 5 − 2 = 3, so the rule holds. Two pairs agreeing is what turns a guess into the rule.
  4. Now apply it to the gap: 11 − 2 = 9.
  5. Check it against the number already after the gap: 9 − 2 = 7, which is what is there. The missing number is 9.

How it works.

  1. 01

    Find the rule first, from two numbers you can actually see — never from the gap.

  2. 02

    7 to 5 is − 2. One pair is a guess, though — check it against another.

  3. 03

    5 − 2 = 3, so the rule holds. Two pairs agreeing is what turns a guess into the rule.

  4. 04

    Now apply it to the gap: 11 − 2 = 9.

  5. 05

    Check it against the number already after the gap: 9 − 2 = 7, which is what is there. The missing number is 9.