Geometric Sequence Formula: Recursive and Explicit

When it comes to understanding geometric sequences, students often struggle with determining which formula is correct. In this article, we will explore the recursive and explicit formulas for geometric sequences and provide guidance on how to determine which one is accurate.

The Recursive Formula for Geometric Sequations

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The recursive formula for a geometric sequence is given by:

an = r × an-1

where an is the nth term of the sequence, r is the common ratio, and an-1 is the (n-1)th term. This formula allows us to calculate each subsequent term in the sequence by multiplying the previous term by the common ratio.

The Explicit Formula for Geometric Sequations

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On the other hand, the explicit formula for a geometric sequence is given by:

an = a1 × r^(n-1)

where an is the nth term of the sequence, a1 is the first term, and r is the common ratio. This formula allows us to calculate any term in the sequence without having to recursively calculate each preceding term.

Determining Which Formula is Correct

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So, which formula is correct? The answer lies in understanding when to use each formula. The recursive formula is useful when we want to calculate a specific term in the sequence, such as finding the 10th term or the 20th term. On the other hand, the explicit formula is more useful when we want to find the nth term of the sequence without having to recursively calculate each preceding term.

In conclusion, both recursive and explicit formulas for geometric sequences are important tools for understanding and working with these types of sequences. By knowing when to use each formula, students can become proficient in calculating terms in geometric sequences and applying them to real-world problems.

Geometric sequence formula recursive and explicit