Series: Mixed Patterns, Missing and Wrong Terms

Difference method

Write the differences between consecutive terms. If they are not constant, take the second difference. Example: 2, 5, 10, 17, 26 → differences 3, 5, 7, 9 (odd numbers).

Multiplication / squares / cubes

Check ×2, ×3 or n², n³ patterns: 1, 8, 27, 64 → cubes. 2, 6, 12, 20, 30 → n(n+1).

Alternate series

Two series interleaved: 3, 10, 6, 20, 12, 40 → odd positions ×2 (3, 6, 12) and even positions ×2 (10, 20, 40).

Letter series

Convert letters to positions: B, E, H, K → 2, 5, 8, 11 (+3). Next is N.

Wrong term

Find the rule using most terms; the single term that breaks it is the wrong one.

Exam tips

1. If numbers grow fast, try multiplication; if slowly, try differences.
2. Memorise squares up to 30 and cubes up to 20.

Analogy

A series is like footprints in the sand. Measure the gap between two steps and you can tell exactly where the next foot will land. If the gaps themselves grow, the walker is speeding up — measure the gap between gaps.