Concept 1 · free preview
How to read a series
Understand
Every series hides one rule. Find the simplest rule that fits all the given terms — then use it for the next term.
| What the series looks like | Check first |
|---|---|
| Growing or falling slowly | Differences |
| Growing fast (roughly doubling or more) | Ratio, or ×k ± c |
| Going up and down (zig-zag) | Alternating operations or two series mixed together |
| Familiar numbers (4, 9, 27, 64…) | Squares, cubes, primes |
Rule
Step 1: look at how fast the terms grow
Step 2: write the differences; if needed, the differences of the differences
Step 3: try ratios or ×k ± c
Step 4: spot special numbers — squares, cubes, primes, Fibonacci
Remember
Know squares up to 30², cubes up to 15³ and primes up to 100 — half the questions are solved by these alone.
Common mistake
Deciding the rule from the first two or three terms only. Test the rule on every term.
Check yourself
12, 24, 48, 96 — differences or ratio first?
Answer: Ratio. Each term doubles (×2), so the next is 192.