An arithmetic sequence adds the same number each time. The nth term is a₁ + (n − 1)d. 3, 7, 11, 15 has d = 4, so the tenth term is 3 + 9 × 4 = 39. Sequences as a set are in sequences on ACT Math.
Find d, then jump
Subtract any term from the next one. If that difference is constant, you are in arithmetic, not geometric. To land on term n, you add d a total of (n − 1) times. The sum of the first n terms is n times the average of the first and last term, if the question asks for a sum.
Multiply-by-a-constant lists are in geometric sequences. Consecutive integers are a special arithmetic list with d = 1, in consecutive integers. Formulas as a set are in ACT Math formulas.
The bottom line
Constant difference: arithmetic. aₙ = a₁ + (n − 1)d.
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