patterns and sequences

Question 1

Arithmetic Sequences (Add/Subtract Patterns)

Answer 1

These go up or down by the same number each time.
Example: 3, 6, 9, 12 → Add 3 each time.

Question 2

Geometric Sequences (Multiply/Divide Patterns)

Answer 2

Each number is multiplied or divided by the same factor.
Example: 2, 4, 8, 16 → Multiply by 2 each time.

Divide each number by the previous one to check for a constant ratio.

Use: next term = previous term × common ratio

Question 3

Square/Cube Number Patterns

Answer 3

Numbers are perfect squares or cubes.
Example: 1, 4, 9, 16 → 1², 2², 3², 4²

Check if numbers match square/cube values (e.g. 16 = 4²).

Try mapping numbers to letters (A = 1, B = 2, … Z = 26) if letters are involved.

Question 4

Alternating or Interleaved Patterns

Answer 4

There might be two patterns running in alternate positions.
Example: 1, 4, 2, 8, 3, 16 → odd positions +1, even ×2

Break the sequence into oddandevenpositions
Solve eachpattern separately

Question 5

Fibonacci-Type Sequences

Answer 5

Each term is the sum of the two before it.

Example: 1, 1, 2, 3, 5, 8, 13

What to do:
- Check if: term(n) = term(n−1) + term(n−2)

Question 6

Number–Letter Pair Questions

Answer 6

These involve squares or positions in the alphabet.
Example: 121 = 11² → K (11th letter)

Match square roots to letters using A=1 to Z=26.

Check if numbers are squares/cubes.

Question 7

General tips

Answer 7

Write out differences between terms.

Question 8

General tips 2

Answer 8

Look for symmetry or repetition.

Question 9

General tips 3

Answer 9

Test a few rules (e.g. ×2, +3, square) — don’t be afraid to try.

Question 10

General tips 4

Answer 10

Label letter positions: A=1, B=2, …, Z=26.

Question 11

General tips 5

Answer 11

• Don’t overthink it — many patterns are based on simple operations.