Question

Finding the $n$ th Term of a Sequence In Exercises $37-48,$ write an expression for the apparent $n$ th term $\left(a_{n}\right)$ of the sequence. (Assume that $n$ begins with $1 . )$ $$ 1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots $$

Name: Problem 44, Chapter 9: Precalculus with Limits
Uploaded: 2021-01-23T20:09:17-08:00
Duration: 1 min 48 s
Channel: Aditya Sood
Description: Finding the n th Term of a Sequence In Exercises 37-48, write an expression for the apparent n th term (an) of the sequence. (Assume that n begins with 1 . ) 1, (1)/(2), (1)/(6), (1)/(24), (1)/(120), …

   Finding the $n$ th Term of a Sequence In Exercises
$37-48,$ write an expression for the apparent $n$ th term
$\left(a_{n}\right)$ of the sequence. (Assume that $n$ begins with $1 . )$
$$
1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots
$$

Precalculus with Limits

Ron Larson 3rd Edition

Chapter 9, Problem 44

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Solved by Expert Aditya Sood

01/23/2021

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So, we can write the general term as $\frac{1}{a_n}$. Show more…

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Finding the $n$ th Term of a Sequence In Exercises $37-48,$ write an expression for the apparent $n$ th term $\left(a_{n}\right)$ of the sequence. (Assume that $n$ begins with $1 . )$ $$ 1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots $$

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Key Concepts

Factorial

A factorial, denoted by n!, is the product of all positive integers from 1 to n. Factorials frequently appear in mathematical sequences, series, and combinatorics, particularly when the structure of the terms grows or shrinks in a manner similar to the products seen in factorial computations.

Sequence

A sequence is an ordered list of numbers where each number is called a term. Understanding a sequence involves recognizing the underlying pattern or rule that connects the terms, which often allows for a general expression to describe any term in the sequence.

nth Term Expression

The nth term expression of a sequence is a formula that provides a direct method to calculate the value of any term based on its position n. This approach avoids the need to compute all previous terms and captures the rule defining the sequence.

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