Grade 12 · Theory
Arithmetic sequences
Sequences and series · about 3 min
Arithmetic, geometric and quadratic sequences side by side.An arithmetic sequence adds a constant difference each time — the Grade 12 workhorse.
Key points- General term: Tₙ = a + (n − 1)d, where a is the first term and d the constant difference.
- d = T₂ − T₁ = T₃ − T₂ (check with more than one pair).
- Sum of n terms: Sₙ = n/2[2a + (n − 1)d] or n/2(a + l) when you know the last term l.
- To find how many terms, solve Tₙ = last value for n.
- Common difference (d) — the constant added each time.
EXAM TIP
identify a and d in the first line of your answer — every subsequent formula depends on them.