The sum of the first n terms of a geometric series is a(1 − rⁿ) / (1 − r) when r is not 1. The sequence itself, not the sum, is in geometric sequences.
First term, ratio, count
a = 3, r = 2, n = 4: 3(1 − 16) / (1 − 2) = 45. The nth term is a different leftover, in nth term of a geometric sequence.
The short list is in ACT Math formulas.
The bottom line
Sum: a(1 − rⁿ) / (1 − r). Do not add the terms by hand if n is large.
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