MathGrade 10ages 15–16
🪜 Arithmetic sequence
An arithmetic sequence adds the same gap at every step — but the first term is a starting point, not a jump, which trips up students counting how many times to add the gap.
Try this lesson freeNo card needed. The first lesson is free.
Download on the App StoreWhat your child learns
- The gap between any two neighbouring terms is fixed.
- From the first term to the fifth there are four jumps, because the first is the starting point and not a jump.
- So the gap is added one time fewer than the term's number.
- A negative gap makes the sequence fall.
The mistake most kids make here
Counting the first term as if it were already one step.
Try one question
A sequence starts at 3 and rises by 4. What is the fifth term?
Starts 3, rises 4
- 19
- 23
- 20
Answer
19 — That's it. The first term is not a jump, so there are four and not five.
How Maya teaches it
Your child tells Maya what they did in class. She teaches this topic at her desk, asks questions with tappable answers, and when the answer is wrong she explains why that answer was tempting instead of saying “try again”. She remembers what did not land and comes back to it.
Your child has it when they can: Say the fifth term of a sequence starting at 3 and rising by 4.
How to help at home
The key confusion is between "which term number" and "how many jumps." Getting from the first term to the fifth takes only four jumps, because the first term is where you already are before jumping at all.
Draw five dots in a row on paper, like stepping stones, and label them 1 through 5. Physically count the arrows (jumps) between them: there are only four arrows connecting five stones.
When your child adds the gap five times instead of four, walk back to the stepping-stone picture and count the arrows together out loud: "stone 1 to stone 2 is jump 1... stone 4 to stone 5 is jump 4." Four jumps, five stones.
A sign they've got it: given any term number, they can say how many jumps it takes from the first term without drawing it out, because they've internalized that it's always one fewer than the term number.
Questions parents ask
- Why is it four jumps to the fifth term, not five?
- The first term is the starting point, before any jump happens. Each jump moves you to the next term, so reaching the fifth term from the first takes exactly four jumps.
- What is a common difference in a sequence?
- It's the fixed amount added (or subtracted) at every step of an arithmetic sequence — the same gap between every pair of neighboring terms.
- What happens with a negative common difference?
- The sequence decreases instead of increases, since you're adding a negative number (which is the same as subtracting) at every step.
- How does Maya teach arithmetic sequences?
- Maya has the child count the jumps between terms directly, like stepping stones, so the 'one fewer than the term number' rule comes from counting, not memorizing.
No card needed. The first lesson is free.
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