Geometric Sequence Calculator

Geometric Sequence

a_n = a x r^n-1 OR   r x a ^n-1

In a sequence if the ratio between every two consecutive term is constant then the sequence is known as " Geometric Sequence ".

• nth term (a_n ) = a x r^n-1 (or) a_n = r x a_n-1
• Sum of the first n terms, S_n = a x (rⁿ -1) / (r - 1) when r ≠ 1
  and Sn = na when r = 1.
• Sum of infinite terms, S_∞ = a / (1 - r) when |r| < 1 and S_∞ diverges
  when |r| ≥ 1.

Suppose, 'a ' is the first number and 'r' is the common ratio, then the sequence is of the form a, ar, ar², ar³, ....,