The explicit formula for a geometric sequence | An = a * r^(n-1) | Example and Explanation

Explicit Formula for Geometric Sequence

The explicit formula (also known as the general term or nth term) for a geometric sequence can be expressed as follows:

An = a * r^(n-1)

Where:
– An represents the nth term of the geometric sequence
– a represents the first term of the sequence
– r represents the common ratio between consecutive terms
– n represents the position of the term in the sequence

To find a specific term (An) in a geometric sequence using the explicit formula, you need to know the first term (a), the common ratio (r), and the position (n) of the term in the sequence

The explicit formula (also known as the general term or nth term) for a geometric sequence can be expressed as follows:

An = a * r^(n-1)

Where:
– An represents the nth term of the geometric sequence
– a represents the first term of the sequence
– r represents the common ratio between consecutive terms
– n represents the position of the term in the sequence

To find a specific term (An) in a geometric sequence using the explicit formula, you need to know the first term (a), the common ratio (r), and the position (n) of the term in the sequence.

Let’s illustrate this with an example:
Consider a geometric sequence with a first term (a) of 3 and a common ratio (r) of 2. We want to find the 5th term (An) of this sequence.

Using the explicit formula, we substitute the given values into the formula:

A5 = 3 * 2^(5-1)

Simplifying this expression:

A5 = 3 * 2^4
= 3 * 16
= 48

Therefore, the 5th term of the sequence with a first term of 3 and a common ratio of 2 is 48.

It’s important to note that the explicit formula only works for a geometric sequence. In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio. If the terms are not related by multiplication, then a different type of sequence or formula will be used.

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