Sequences

An arithmetic sequence adds the same number each time; a geometric sequence multiplies by the same number. Find the pattern, then the formula.

1. Check differences first; if they are equal, it is arithmetic: aₙ = a₁ + (n − 1)d.
2. If the ratios are equal, it is geometric: aₙ = a₁ × r⁽ⁿ⁻¹⁾.
3. For repeating patterns, divide the term number by the length of the cycle and use the remainder.

• Using n instead of n − 1 steps.
• In a repeating cycle, a remainder of 0 means the last item of the cycle, not the first.

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