①TERM RULE
$T_n$: substitute $n$ · $a=T_1$ · $d=T_2-T_1$
②GENERAL TERM
$T_n=a+(n-1)d$ · which term? set $T_n=$ value, solve for $n$
③SPECIAL
consecutive: $T_2-T_1=T_3-T_2$ · two terms → two equations → $a,d$
④SERIES
$S_n=\dfrac{n}{2}\{2a+(n-1)d\}$
⑤Sn BACKWARDS
$a=S_1$ · $T_2=S_2-S_1$ · $d=T_2-T_1$
⑥QUADRATIC
2nd diff constant · $T_n=an^2+bn+c$ · $a=\dfrac{\text{2nd diff}}{2}$ · use $T_1,T_2$