Geometric Sequence Calculator

Instructions: This algebraic calculator will allow you to compute elements of a geometric sequence. A geometric sequence has the form:

\[a_1, a_1 r, a_1 r^2, ...\]

You need to provide the first term of the sequence (\(a_1\)), the constant ratio between two consecutive values of the sequence (\(r\)), and the number of steps further in the sequence(\(n\)). Please provide the information required below:

First term (\(a_1\))
Ratio (\(r\))
Number of steps (\( n \))

What is a Geometric Sequence?

Learn more about geometric sequences so you can better interpret the results provided by this calculator: A geometric sequence is a sequence of numbers \(a_1, a_2, a_3, ....\) with the specific property that the ratio between two consecutive terms of the sequence is ALWAYS constant, equal to a certain value \(r\). The value of the \(n^{th}\) term of the arithmetic sequence, \(a_n\) is computed by using the following formula:

\[a_n = a_1 r^{n-1}\]

The above formula allows you to find the find the nth term of the geometric sequence. This means that in order to get the next element in the sequence we multiply the ratio \(r\) by the previous element in the sequence. So then, the first element is \(a_1\), the next one is \(a_1 r\), the next one is \(a_1 r^2\), and so on.

For this type of sequence, the ratio between two consecutive values in the sequence is constant. If you are dealing with the case in which the difference between any two consecutive values of the sequence is constant, then you use use our arithmetic sequence calculator instead.

On the other hand, if you want to add an infinite geometric series, you can use this geometric series calculator .

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