The formula card
A standard method from Arithmetic and geometric sequences: the steps.
Steps
| AS (add d each time) | GS (multiply by r each time) | |
|---|---|---|
| general term | Tₙ = a + (n − 1)d | Tₙ = arⁿ⁻¹ |
| sum of n terms | Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l) | Sₙ = a(rⁿ − 1)/(r − 1), r ≠ 1 |
| sum to infinity | — | S∞ = a/(1 − r), only if −1 < r < 1 |
| test | T₂ − T₁ = T₃ − T₂ | T₂/T₁ = T₃/T₂ |
Why n − 1: to get from the 1st term to the nth term you take n − 1 steps.
For the whole topic, read Arithmetic and geometric sequences: key points, common mistakes and how the DSE tests it.