Question

Find the $n$ th term of each geometric sequence. $$\frac{16}{3}, 4,3, \frac{9}{4}, \dots$$

Name: Problem 30, Chapter 10: Intermediate Algebra
Uploaded: 2020-07-20T07:54:46-08:00
Duration: 1 min 13 s
Channel: Ankit Gupta
Description: Find the n th term of each geometric sequence. (16)/(3), 4,3, (9)/(4), …

   Find the $n$ th term of each geometric sequence.
$$\frac{16}{3}, 4,3, \frac{9}{4}, \dots$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 10, Problem 30

Instant Answer

Solved by Expert Ankit Gupta

07/20/2020

Step 1

The first term is the first number in the sequence, which is $\frac{16}{3}$. The common ratio is the factor by which each term is multiplied to get the next term. In this case, we can find the common ratio by dividing the second term by the first term, or the Show more…

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Find the $n$ th term of each geometric sequence. $$\frac{16}{3}, 4,3, \frac{9}{4}, \dots$$

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Key Concepts

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 type of sequence is fundamental in algebra as it models exponential growth or decay processes in various contexts.

Common Ratio

The common ratio is the fixed number that each term of a geometric sequence is multiplied by to obtain the next term. It is found by dividing any term in the sequence by the term immediately preceding it, and it is essential for determining the behavior and formula of the sequence.

Nth Term Formula

The nth term of a geometric sequence is calculated using the formula a? = a? × r^(n-1), where a? is the first term and r is the common ratio. This formula provides a direct way to find any term in the sequence without having to compute all previous terms.

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