Work out the nth term and the sum of the first terms in an arithmetic or geometric sequence.
An arithmetic sequence has a fixed number d that's added for each new term, for example 2, 5, 8, 11, … with d = 3. The formulas are:
A geometric sequence has a fixed number r that each term is multiplied by, for example 2, 6, 18, 54, … with r = 3. The formulas are:
In an arithmetic sequence, the same fixed number is added for each new term (for example +3 each time). In a geometric sequence, each term is multiplied by the same fixed number (for example ×3 each time), which gives much faster growth.
Then the terms get smaller and smaller each time, and the sum approaches a fixed limit even if you add up infinitely many terms. This calculator works out the sum of a finite number of terms n, not the infinite sum.
Arithmetic sequences are used, among other things, to calculate fixed, even changes (like loan payments or saving a fixed amount), while geometric sequences are used for compound interest, population growth and other processes with a percentage change per period.