A TikTok clip doubles its views every day — 2,000 on Monday, 4,000 on Tuesday — and by Friday the creator is staring at six figures. In plain words, a geometric sequence multiplies by a fixed ratio each step, so the nth term is the first term times the ratio raised to the n−1 power: an = a1 × r^(n−1). The running total of the first n terms is a1 × (1 − r^n) / (1 − r). Ten doublings from 1,000 views reach 512,000 on the tenth day alone, with over a million views accumulated — the exponent does all the heavy lifting. Investors watching compound growth, biologists modeling bacteria, and marketers projecting viral reach all ride this curve; anything growing by a percentage rather than a fixed amount is geometric.

This calculator finds any term and the running total. Type the starting value into the First Term (a1) box, say 1000, the multiplier into the Common Ratio (r) box, say 2, and how many terms into the Number of Terms (n) box, say 10. Read the Nth Term (an) box for the last value — 512,000 — and the Sum of N Terms (Sn) box for the accumulated total of 1,023,000.

With the pre-filled defaults — First Term (a1) 1, Common Ratio (r) 2, Number of Terms (n) 5 — the Geometric Sequence Calculator returns Nth Term (an) 16.0000, Sum of N Terms (Sn) 31.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.