Summing an Arithmetic Series (HSC SSCE Mathematics Advanced): Flashcards

$S_n$

$S_n = \frac{1}{2}n(a + \ell)$

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

$S_n = \frac{1}{2}n(a + \ell)$ (first formula)

$(a + \ell)$ (first term + last term)

$\ell = T_n = a + (n-1)d$

$b - a + 1$

Sum can eventually become negative

Use $T_n = a + (n-1)d$, solve for $n$

Set up simultaneous equations to find $a$ and $d$