Geometric sequences calculator

This tool can help you find $n^{th}$ term and the sum of the first $n$ terms of a geometric progression. Also, this calculator can be used to solve more complicated problems. For example, the calculator can find the first term ($a_1$) and common ratio ($r$) if $a_2 = 6 $ and $a_5 = 48$. The calculator will generate all the work with detailed explanation.

Basic calculator Solve for a₁ and r Solve for n

Geometric Sequences Calculator

Find n - th term and the sum of the first n terms.
help ↓↓ examples ↓↓ tutorial ↓↓

First term (a₁):

Common ratio ( r ) :

Number of terms ( n ) :

Choose what to compute

a_n (the n-th term)

S_n ( the sum of the first n terms )

Settings:

Find approximate solution

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Geometric Sequences Calculator

Find first term and/or common ratio.
help ↓↓ examples ↓↓ tutorial ↓↓

Enter values in two out of four rows.

First term ( a₁ ) :

Common ratio (r):

Enter n-th term

$a~(~$ $~)=~$

Enter n-th term

$a~(~$ $~)=~$

Settings:

Find approximate solution

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Get Widget Code

Geometric Sequences Calculator

Find number of terms.
help ↓↓ examples ↓↓ tutorial ↓↓

Enter values in three out of four rows.

First term (a₁) *

Common ratio (r) *

Enter n-th term

$a~(~n~)~=~$

Sum of first n-terms

$S~(~n~)~=~$

Settings:

Find approximate solution

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Get Widget Code

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Examples

ex 1:

Find the sum $\sum\limits_{i=0}^{12} 3 \cdot 2^i $.

ex 2:

Find the common ratio if the fourth term in geometric series is $\frac{4}{3}$ and the eighth term is $\frac{64}{243}$.

example 3:ex 3:

The first term of a geometric progression is 1, and the common ratio is 5 determine how many terms must be added together to give a sum of 3906.

Related calculators

Arithmetic sequences calculator

nth term of a sequence

About this calculator

Definition:

Geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant. The constant is called the common ratio ($r$).

Formulas:

The formula for finding $n^{th}$ term of a geometric progression is $\color{blue}{a_n = a_1 \cdot r^{n-1}}$, where $\color{blue}{a_1}$ is the first term and $\color{blue}{r}$ is the common ratio. The formulas for the sum of first $n$ numbers are $\color{blue}{S_n = a_1 \frac{1-r^n}{1-r}}$.

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