Geometric Sequence Calculator

The first number
common difference (r)
Nth term to obtain

Geometric Sequence

an = a x rn-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 (an ) = a x rn-1 (or) an = r x an-1
  • Sum of the first n terms, Sn = 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, ....,

Example:
Find a15 of a geometric sequence if a13 = -8 and r = 1/3.
Solution:
By the formula of geometric sequence,
a14 = r a13 = (1/3) (-8) = -8/3
a 15 = r a14 = (1/3) (-8/3) = -8/9.
Therefore, a15 = -8/9.