Geometric Sequence Calculator

Geometric sequence calculator calculates the particular term of the geometric sequence and the total sum of all the sequence numbers, by the giving value of the first term, and common ratio.

What is Geometric Sequence

A geometric sequence is a sequence of numbers that has a common ratio between consecutive numbers.

For example,
if there is a sequence of numbers: 2, 6, 18, 54, 162, 486,
we need to check to see if there is a common ratio, since
6/2=3
18/6=3
54/18=3
162/54=3
486/162=3
There is a common ratio of 3, then it is a geometric sequence.

Geometric Sequence Formula

a_n = a₁ x r^n-1

while
a_n = last number of the sequence
a₁ = first number of the sequence
r = the common ratio.
n = the number of terms.

Sum of Geometric Sequence Number

The sum of all of the geometric numbers is:
a₁+a₂...+a_n

by calculating, it equals:

a₁xrⁿ-1/r-1

For example, if there is a total of 6 geometric sequence numbers, the first number of the sequence is 2, the common ratio is 3, and the last number of the sequence is 486.

The sum of all of the numbers is calculated as:
a₁xrⁿ-1/r-1
=2x3⁶-1/3-1
=2x729-13-1
=728.