# Finding the Explicit Formula of a Geometric Sequence: Example 6

## Topic

Sequences and Series

## Description

Methodology for Finding the Explicit Formula

1. Identify the First Term: The first term of the sequence is denoted as a1.
2. Determine the Common Ratio: The common ratio r is found by dividing the second term by the first term.
3. Write the Explicit Formula: The nth term of a geometric sequence can be found using the formula:

an = a1•r(n - 1)

where an is the nth term, a1 is the previous term, r is the common ratio, and n is the term number.

Given Sequence

Sequence: [7, 28, 112, 448, 1792]

First term (a₁) = 7

Common ratio (r) = 28 / 7 = 4

Explicit formula: an = 7•4(n - 1)

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Common Core Standards CCSS.MATH.CONTENT.HSF.BF.A.2 9 - 11 Algebra     • Sequences and Series         • Sequences 2022 geometric sequence, explicit formula