Geometric Sequence Calculator

Easily calculate terms of a geometric sequence. Enter the first term, common ratio, and number of terms to generate the sequence.

First Term (a₁):

Common Ratio (r):

Number of Terms (n):

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Result

Understanding Geometric Sequences

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Formula:

The $n$-th term ($a_n$) of a geometric sequence is given by the formula:

$$a_n = a_1 \cdot r^{(n-1)}$$

$a_n$ is the $n$-th term.
$a_1$ is the first term.
$r$ is the common ratio.
$n$ is the term number.

Example:

Consider a geometric sequence with the first term $a_1 = 2$ and common ratio $r = 3$. The first few terms are:

$a_1 = 2$
$a_2 = 2 \cdot 3 = 6$
$a_3 = 6 \cdot 3 = 18$
$a_4 = 18 \cdot 3 = 54$
and so on...

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