A geometric sequence multiplies by the same number each time. The nth term is a₁ times r to the (n − 1). 2, 6, 18, 54 has r = 3, so the fifth term is 2 × 3⁴ = 162. Sequences as a set are in sequences on ACT Math.
Find r, then raise
Divide any term by the one before it. If that ratio is constant, you are in geometric, not arithmetic. Negative r makes the signs alternate. Exponential growth uses the same multiply-repeatedly idea, in exponential growth and decay.
Add-a-constant lists are in arithmetic sequences. Formulas as a set are in ACT Math formulas.
The bottom line
Constant ratio: geometric. aₙ = a₁ × r^(n − 1).
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