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

It has a common ratio between terms.

$u_n = ar^{(n-1)}$

Divide a term by its previous term.

$S_n = a(1 - r^n) / (1 - r)$

Subtract $rS_n$ from $S_n$ and simplify.

$u_n = 3 \cdot (-4)^{(n-1)}$

$a$ is the first term of the sequence.

Solve $ar^{(n-1)} < 10,000$ using logarithms.

$r = 32 / 0.5 = 64$; ratio doubles each term.

$a = 0.5 / 4 = 0.125$