How Sequences Questions Get Harder From Grade 10 to Grade 12 — And What Stays the Same

Grade 10: Number Patterns — Spot It, Describe It

At Grade 10, the topic is called number patterns, and the core skill is purely about recognising a pattern in a sequence of numbers and describing the rule that generates it — usually finding a formula for the general term, Tn, from a given sequence of numbers or a described real-world situation. Questions typically give you the first several terms and ask you to find a specific term further along, or to find the general term itself. There is no formal distinction yet between "arithmetic" and "geometric" — you're working with the pattern directly.

Grade 11: Two Named Types, With Their Own Formulas

Grade 11 introduces formal vocabulary: arithmetic sequences (constant difference between terms) and geometric sequences (constant ratio between terms), each with its own general term formula. The genuinely new skill here is not the pattern-spotting from Grade 10 — it's recognising *which type* of sequence you're looking at from the wording or the numbers given, since the two types require different formulas and behave very differently (geometric sequences can grow or shrink much faster). A common mistake at this level is applying the arithmetic formula to a geometric sequence, or vice versa, because the student didn't pause to check which type it was before reaching for a formula.

Grade 12: Series, Sigma Notation, and Sums to Infinity

Grade 12 adds series — the sum of a sequence's terms, rather than just an individual term — along with sigma (Σ) notation as a compact way of writing that sum, and the concept of a sum to infinity for a converging geometric series (only possible when the common ratio's absolute value is less than 1). This is where the topic becomes noticeably more demanding: you now need to recognise whether a question is asking for a specific term (carried over from Grade 10 and 11) or the sum of a run of terms (new), and for geometric series specifically, whether it's asking for a sum to infinity — which requires checking the convergence condition first, a step many students skip entirely.

The One Skill That Carries Through All Three Grades

Across all three grades, the single most important habit is the same: before reaching for any formula, identify exactly what you're being asked to find. Is it a specific term (Tn), or a sum (Sn)? Is the sequence arithmetic or geometric? Is a sum to infinity even valid here, or does the question involve a finite number of terms? Students who lose marks in this topic at every grade level almost always lose them the same way — jumping to a formula before confirming which formula actually applies to what's being asked.

See the full breakdown of question types for your grade on the instruction word guides and topic guides.