Write an expression for the apparent n th term (an) of the sequence. (Assume that n begins with

Name: Problem 47, Chapter 9: Precalculus
Uploaded: 2021-02-07T14:20:59-08:00
Duration: 1 min 7 s
Channel: Anurag Kumar
Description: 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), …

step 1 In this here problem of sequence we have given the sequence that is one half 1 divided with 6 1

Question

Write an expression for the apparent $n$ th term $\left(a_{n}\right)$ of the sequence. (Assume that $n \text { begins with } 1 .)$ $$1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots$$

   Write an expression for the apparent $n$ th term $\left(a_{n}\right)$ of the sequence. (Assume that $n \text { begins with } 1 .)$
$$1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots$$

Precalculus

Ron Larson 10th Edition

Chapter 9, Problem 47

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Solved by Expert Anurag Kumar

02/07/2021

Step 1

Step 1: First, we observe the given sequence: $1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots$ Show more…

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Write an expression for the apparent $n$ th term $\left(a_{n}\right)$ of the sequence. (Assume that $n \text { begins with } 1 .)$ $$1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}, \frac{1}{120}, \dots$$

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Key Concepts

Sequence

A sequence is an ordered list of numbers that follows a specific rule or pattern. It can be defined either by an explicit formula for its nth term or by a recursive relationship, which makes understanding the underlying pattern essential for deeper insights into the sequence.

nth Term Formula

The nth term formula provides a direct way to calculate any term in the sequence based on its position (n) without having to compute all previous terms. This explicit expression is crucial for analyzing the properties of the sequence and predicting future terms efficiently.

Factorial

The factorial function, denoted by n!, is the product of all positive integers from 1 to n. It is widely used in combinatorics to count arrangements and appears in series and sequence definitions, particularly when the terms involve rapid growth or decay as n increases.

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