Find the nth term and sum of an arithmetic or geometric sequence.
Arithmetic sequences add the same value (the common difference, d) each step — like 2, 5, 8, 11. Geometric sequences multiply by the same value (the common ratio, r) each step — like 2, 6, 18, 54. Pick the matching mode and enter that constant in the second field.
For a geometric sequence with |r| < 1, each term shrinks toward zero and the running total converges to a finite value — a1/(1−r). This only makes sense when the ratio's absolute value is less than 1, so it's hidden otherwise (and never shown for arithmetic sequences).
A geometric sequence with |r| > 1 grows without bound, so the term or sum can exceed what a standard floating-point number can represent — the calculator shows ∞ in that case instead of a misleading huge number.