/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Given the general term of each s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 20

Given the general term of each sequence, find each of the following. \(a_{n}=4 n^{2}-9\) a) the first term of the sequence b) the fourth term c) the 13 th term

Short Answer

Expert verified
The first term of the sequence is -5, the fourth term is 55, and the 13th term is 667.

Step by step solution

01

Determine the Formula for the nth Term

The formula for the nth term in the sequence is provided as \(a_n = 4n^2 - 9\).
02

Step 2a: Find the First Term (n=1)

To find the first term, substitute n=1 into the formula: \(a_1 = 4(1)^2 - 9\). Calculate the result: \(a_1 = 4(1) - 9 = 4 - 9 = -5\) The first term in the sequence is -5.
03

Step 2b: Find the Fourth Term (n=4)

To find the fourth term, substitute n=4 into the formula: \(a_4 = 4(4)^2 - 9\). Calculate the result: \(a_4 = 4(16) - 9 = 64 - 9 = 55\) The fourth term in the sequence is 55.
04

Step 2c: Find the 13th Term (n=13)

To find the 13th term, substitute n=13 into the formula: \(a_{13} = 4(13)^2 -9\). Calculate the result: \(a_{13} = 4(169) - 9 = 676 - 9 = 667\) The 13th term in the sequence is 667.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the binomial theorem to expand each expression. $$\left(t^{2}-\frac{1}{2} u\right)^{4}$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=20, r=-\frac{3}{4}$$

Evaluate each binomial coefficient. $$\left(\begin{array}{l}5 \\\0\end{array}\right)$$

Evaluate each binomial coefficient. $$\left(\begin{array}{l}3 \\\1\end{array}\right)$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$\frac{7}{2}, \frac{7}{4}, \frac{7}{8}, \frac{7}{16}, \dots$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.