A progression is a list of numbers with a rule. SPM Add Maths asks you to find a term, add up terms, and decide which rule a story describes.
How do the four lessons connect?
The lessons build in one order, and each leans on the one before it.
- Arithmetic progressions add the same amount each step.
- Geometric progressions multiply by the same number each step.
- The sum to infinity extends the geometric case when the ratio is small.
- Translating payment or growth patterns uses all three in word problems.
How do I tell which progression it is?
Here is an original test with three sequences. Write down the gaps and the ratios between neighbouring terms.
| Sequence | Differences | Ratios | Type |
|---|---|---|---|
| 5, 8, 11, 14 | 3, 3, 3 | 1.6, 1.375, 1.27 | Arithmetic, d = 3 |
| 5, 10, 20, 40 | 5, 10, 20 | 2, 2, 2 | Geometric, r = 2 |
| 5, 8, 12, 17 | 3, 4, 5 | 1.6, 1.5, 1.42 | Neither |
The third row shows why the test has two parts. Differences that grow are not constant, and ratios that shrink are not constant either, so neither rule applies.
This two-step check is the first thing to do with any unfamiliar list. Errors in progression questions start with assuming the type before testing it.
Who should start where?
A student who is new to the chapter starts with arithmetic progressions, because the arithmetic is gentle. A student who is solid on those moves to geometric progressions, where a power replaces a multiplication.
A student who can already do both but loses marks on stories starts with the last lesson. After any lesson, the practice set mixes the types so that choosing the progression becomes part of the question.
If indices or fractions slow you down, the algebra step repair trainer and the word-problem structure worksheet are helpful companions. Progressions sit beside functions and quadratic functions in Form 4.
Will the pace suit a student who needs to revisit algebra?
Yes. Each lesson uses small numbers first and shows each algebra step, so the new idea is not hidden under heavy arithmetic. A student who needs more time can do the lessons in order and repeat the self-check question before moving on.
When is tuition worth considering?
Free lessons explain the formulas. A one-to-one teacher watches you meet a story you have not seen and shows how to spot its pattern.
Read about online one-to-one Additional Mathematics tuition or return to the Additional Mathematics guide.