Question

Show that each sequence is geometric. Then find the common ratio and list the first four terms. $$ \left\{f_{n}\right\}=\left\{3^{2 n}\right\} $$

Name: Problem 16, Chapter 13: Algebra and Trigonometry
Uploaded: 2021-08-08T15:12:05-08:00
Duration: 2 min 32 s
Channel: Yujie Wang
Description: Show that each sequence is geometric. Then find the common ratio and list the first four terms. {fn}={3^2 n}

   Show that each sequence is geometric. Then find the common ratio and list the first four terms.
$$
\left\{f_{n}\right\}=\left\{3^{2 n}\right\}
$$

Algebra and Trigonometry

Michael Sullivan 11th Edition

Chapter 13, Problem 16

Instant Answer

Solved by Expert Yujie Wang

08/08/2021

Step 1

We can do this by substituting $n=1$ into the formula for the sequence. This gives us $f_1 = 3^{2(1)} = 3^2 = 9$. Show more…

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Show that each sequence is geometric. Then find the common ratio and list the first four terms. $$ \left\{f_{n}\right\}=\left\{3^{2 n}\right\} $$

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Key Concepts

Nth Term Formula

The nth term formula for a geometric sequence is given by a_n = a_1 * r^(n - 1), where a_1 is the first term and r is the common ratio. This formula is essential because it provides a method to directly calculate any term in the sequence without needing to compute all the previous terms.

Common Ratio

The common ratio in a geometric sequence is the constant factor that is used to obtain each successive term from the previous term. It is determined by dividing any term in the sequence by the preceding term, and it is a crucial concept because it dictates how the sequence grows or decays.

Geometric Sequence

A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant factor known as the common ratio. This property allows the sequence to be expressed in a compact form using exponential notation, making it easier to analyze and manipulate.

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