Summing a Geometric Series (HSC SSCE Mathematics Advanced): Flashcards

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

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

First term, common ratio, number of terms

To avoid negative numbers in the denominator

$S_n = an$

Would divide by zero (denominator $r - 1 = 0$)

Multiply sum by $r$, then subtract original equation

Most terms cancel, leaving only first and last terms

Trial-and-error or using logarithms

Compound interest and exponential growth patterns