Modelling with Sequences & Series (AQA A-Level Mathematics): Flashcards

Constant difference between consecutive terms

$a_n = a_1 + (n-1)d$

$S_n = \frac{n}{2}(2a_1 + (n-1)d)$

Constant that multiplies previous term

$a_n = a_1 r^{n-1}$

$S_n = \frac{a_1(1-r^n)}{1-r}$

$S_\infty = \frac{a_1}{1-r}$

$|r| < 1$

$S_n = \frac{n}{2}(a_1 + a_n)$

Arithmetic sequence