Sequences and series (internal)
Internal 2 credits Arithmetic Geometric Sums Infinite series ModellingAS 91258, 2 credits. Arithmetic and geometric sequences, their sums, and the infinite geometric sum — applied to a real situation like savings, depreciation, repayments or population.
1 Reading the notation
Five named method areas, and a note that solving may require logarithms.📖 Terms the schedule grades you on
2 terms- Apply methods (Achieved)
- Select and use methods; demonstrate knowledge of concepts and terms; communicate using appropriate representations.
- Named methods (note 4)
- General term; partial sum; sum to infinity; finding a, d or r; finding the number of terms.
2 What the grades require
The same ladder every L2 maths internal uses.| Grade | What it takes | The half people drop |
|---|---|---|
| Achieved | Select and use methods; know the concepts and terms; communicate with appropriate representations | Showing no working — the method IS the evidence |
| Merit | A logical sequence of steps, connecting concepts, or forming and using a model | The "and also": relate findings back to the context |
| Excellence | Devise a strategy, build a chain of reasoning or a proof, or form a generalisation | The "and also": correct mathematical statements, or a stated insight |
Both Merit and Excellence are "one or more of … AND ALSO …". A perfect answer that never interprets its result in context cannot pass the Achieved ceiling.
3 The four formulas
Identify the type first — it decides which pair of formulas applies.What to have memorised
Arithmetic nth term aₙ = a + (n − 1)d n − 1, not n Arithmetic sum Sₙ = n/2 (2a + (n − 1)d) Or n/2 (a + l) Geometric nth term aₙ = a·rⁿ⁻¹ r is the growth/decay factor Geometric sum Sₙ = a(rⁿ − 1)/(r − 1) Use a(1 − rⁿ)/(1 − r) when r < 1 Infinite geometric sum S∞ = a/(1 − r) ONLY if |r| < 1 — state the condition4 Solving, then interpreting in context
The context step is where the credits actually sit in a 2-credit standard. ✕15% depreciation is r = 0.85
A decay of 15% per year means the value RETAINED is 85%, so r = 0.85. Using r = 0.15 models losing 85% a year. Convert the percentage into the multiplier and say which you did.Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.