Sequence Items on the ACT and Their Absence from the Digital SAT

Sequences show up here but not on every math test, so if your prep came from somewhere else, this can feel brand new. A sequence is just an ordered list of numbers following a rule. Arithmetic sequences add the same amount each step; geometric sequences multiply by the same factor each step. The test rarely says 'sequence' outright. Instead it tells a story: a theater with rows of seats, a savings account getting a weekly deposit, a bacteria colony doubling every hour. Your job is to recognize the pattern underneath the plot.

The giveaway is in the verb. If something gets a fixed amount added or removed each step, that is arithmetic, and the nth term is the starting value plus (n minus 1) times the common difference. If something gets multiplied by a fixed factor each step, that is geometric, and the nth term is the starting value times the common ratio raised to the (n minus 1) power. Once you tag the story correctly, you plug numbers into one of these two formulas and you are done, no need to write out every term by hand.

Geometric sequences are close cousins of exponential functions, and that connection matters. An exponential function like f(t) = a times r^t gives a smooth curve for any input t, including fractions and decimals. A geometric sequence is that same function, but you only ever look at it at whole-number steps: t = 0, 1, 2, 3. The common ratio r in the sequence is exactly the base r in the exponential. Seeing sequences as exponential functions sampled at integers ties this topic straight back to exponential growth and decay.