Calculating aGeometric Sequence: Finding the Nth Term with Example Calculation

Explicit Formula for Geometric Sequence

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant value called the common ratio (r)

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant value called the common ratio (r). The explicit formula for a geometric sequence is given by:

an = a1 * r^(n-1)

where:
– an is the nth term in the sequence
– a1 is the first term in the sequence
– r is the common ratio
– n is the position of the term in the sequence

To find the value of any term in the sequence, you need to know the first term (a1), the common ratio (r), and the position of the term in the sequence (n).

Let’s illustrate this with an example:
Given a geometric sequence with a first term a1 = 2 and a common ratio r = 3, we want to find the 6th term (n=6) in the sequence.

Using the explicit formula:
a6 = a1 * r^(n-1)
a6 = 2 * 3^(6-1)
a6 = 2 * 3^5
a6 = 2 * 243
a6 = 486

So, the 6th term in this geometric sequence is 486.

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