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

A sequence with a constant difference between terms.

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

$S_n = n/2(2a_1 + (n-1)d)$ or $S_n = n/2(a_1 + a_n)$

Each term is found by multiplying the previous term.

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

$S_n = a_1(1 - r^n)/(1 - r)$ for $r ≠ 1$

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

Use a geometric sequence for exponential growth.

Total savings $T_n = \frac{n}{2}(2a_1 + (n-1)d)$

$R_n = P(1+r)^n - M \cdot \frac{(1+r)^n - 1}{r}$