Number Sequence Calculator | Arithmetic & Geometric Solver
Solve arithmetic and geometric sequences, find the nth term, common ratio/difference, sum of series, and auto-detect patterns from any list of numbers.
Term at Index a_n (n = 10)
19
Series Sum S_n
100
Sequence Terms (10 shown)
a1:1
a2:3
a3:5
a4:7
a5:9
a6:11
a7:13
a8:15
a9:17
a10:19
Progression Rate of Growth Curve
a1: 1
a1a2: 3
a2a3: 5
a3a4: 7
a4a5: 9
a5a6: 11
a6a7: 13
a7a8: 15
a8a9: 17
a9a10: 19
a10Rate curve plots indices up to first 15 values relative to peak heights. Negative values are color-coded red.
Step-by-step Mathematical Derivations
Formula: a_n = a_1 + (n - 1) * d
a_10 = 1 + (10 - 1) * 2 = 19
Sum Formula: S_n = (n / 2) * (a_1 + a_n)
S_10 = (10 / 2) * (1 + 19) = 100