Arithmetic Sequence Calculator
The nth term and the sum of the first n terms, from the first term and common difference.
The formulas
aₙ = a₁ + (n-1)d Sₙ = n(a₁ + aₙ)/2
The sum formula is young Gauss's classroom trick: pair the first term with the last, the second with the second-to-last, and every pair adds to the same value; n/2 pairs times that value is the sum. 1 to 100 gives 50 pairs of 101: 5,050.
Spotting an arithmetic sequence
Consecutive differences are constant. 5, 8, 11, 14 is arithmetic with d = 3; the 20th term is 5 + 19×3 = 62 and the first twenty sum to 670. If the RATIO is constant instead, you want the geometric sequence calculator.